PERMUTAION AND COMBINATION Question for CAT (Selection and grouping)
- Jul 22
- 9 min read
PERMUTAION AND COMBINATION Question for CAT
Q.1 16 persons shake hands with one another in a party. How many shake hands took place?
a.120
b.240
c.480
d.None of the above
Q.2 Calculate in how many ways can a set of five players be formed out of a total of ten players such that two particular players should be involved in each set?
a.56
b.60
c.72
d.75
Q.3 Ten students are participating in the race. In how many different ways can the first three prizes be won?
a.10C3
b.10P3
c.103
d.310
Q.4 A man tries to send invitation to 6 of his friends through 3 servants. Find the number of possible ways that the invitation card can be sent.
a.216
b.729
c.6! × 3!
d.None of the above
Q.5 The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is:
a.D(15)
b.15!
c.30C15
d.30P15
Q.6 Five students are to be arranged on five chairs for a photograph. Three of these are girls and the rest are boys. Find the total number of arrangements, in which three girls are together.
a.36
b.120
c.12
d.None of the above
Q.7 From a group of 5 men and 10 women, a committee has to formed of 5 members in which at least 4 men are required. The committee can be formed in .................... ways.
a.50
b.15C5
c.51
d.None of the above
Q.8 5 Indian and 5 American couples meet at a party and shake hands. If no wife shakes hands with her husband and no Indian wife shakes hands with a male, then find the number of hand shakes that take place in the party?
a.120
b.240
c.480
d.None of the above
Q.9 A shop owner has an unlimited supply of 8 different types of flowers. If a customer asks for a five flower arrangement such that the arrangement should start and end with the same type of flower, then in how many ways the arrangement can be made by the shop owner?
a.8C4 x 3!
b.83
c.84
d.8C4 x 4C1 x 3!
Q.10 In how many ways can be select 5 cards from a card pack such that all 4 suits appear?
a.52728
b.405646
c.685464
d.4056
Q.11 In a chess tournament, all participants were to play one game with the other. Two players fell ill after having played 3 games each. If total number of games played in the tournament is equal to 84, then total number of participants in the beginning was equal to:
a.14
b.15
c.16
d.18
Q.12 There is a straight table with a capacity of 9 members and they have to sit only on one side of the table. Arrange 4 boys and 5 girls such that the boy must have two girls adjacent to the boy (on either side). Find the total number of arrangements.
a.1840
b.2160
c.2880
d.6240
Q.13 The number of ways in which a mixed double game can be arranged from amongst 9 married couples, if no husband and wife play in the same game is:
a.1512
b.1514
c.3024
d.3028
Q.14 From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is:
a.At least 750 but less than 1000
b.At least 1000
c.Less than 500
d.At least 500 but less than 750
Q.15 A box contains 4 different pink balls and 5 different blue balls. In how many ways can you make a selection so as to take at least 1 pink ball and 1 blue ball?
a.(24 - 1) × (25 - 1)
b.(29 - 1)
c.(9! - 1)
d.None of the above
Q.16 In how many ways can a committee of 5 persons be formed from 6 gents and 4 ladies so that there is at least one lady in the committee?
a.246
b.10C5
c.10P5
d.None of the above
Q.17 There are 280 ways of forming a group of (x + 2) men and 3 women out of a total of 8 men and 5 women. Find the value of x.
a.2
b.3
c.4
d.6
Q.18 Three men have 4 coats, 5 waist coats and 6 caps. The number of ways they can wear them is:
a.15P3
b.4C3 × 5C3 × 6C3
c.180
d.4P3 × 5P3 × 6P3
Q.19 An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that atmost three of them are red is .................... .
a.420
b.455
c.490
d.None of these
Q.20 Kavita has 10 friends and she wants to invite 6 of them to a party. How many times will 3 particular friends always attend the party?
a.10C6
b.10C3
c.7C3
d.None of the above
Q.21 A double-decker bus has 5 empty seats in the up-stair and 5 empty seats in the down stair. 10 people board the bus of which 2 are old people and 3 are children. The children refuse to take seats down stair while old people insist to stay down-stair. In how many different arrangements can be 10 people take their seats in the bus?
a.144000
b.146000
c.146400
d.None of these
Q.22 The number of ways in which 3 distinct numbers in AP can be selected from 1, 2, 3, ….24 is
a.132
b.572
c.264
d.150
Q.23 The number of ways of arranging 7 persons (A, B, C and D among them), in a row so that, A, B, C and D are always in the order A – B - C- D (not necessarily together) will be
a.24
b.5040
c.210
d.None of the above
Q.24 The number of ways of dividing 10 books into 3 group of 5,3,2, books respectively is
a.10C5 . 5C3 . 2C2
b.10C5
c.10!
d.None of the above
Q25Find the number of ways of dividing 12 people among three groups such that one group has 6 members and each of the other two groups has 3 members
a.12C6
b.12P6
c.12C6 . 6C3. 3C
d.12C6 . 6C3. 3C3 / 2!
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
A | A | B | B | B | A | C | D | C | C |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
B | C | A | B | A | A | C | D | C | C |
21 | 22 | 23 | 24 | 25 | |||||
A | A | C | A | D |
Q.1 16 persons shake hands with one another in a party. How many shake hands took place?
a.120
b.240
c.480
d.None of the above
Q.2 Calculate in how many ways can a set of five players be formed out of a total of ten players such that two particular players should be involved in each set?
a.56
b.60
c.72
d.75
Q.3 Ten students are participating in the race. In how many different ways can the first three prizes be won?
a.10C3
b.10P3
c.103
d.310
Q.4 A man tries to send invitation to 6 of his friends through 3 servants. Find the number of possible ways that the invitation card can be sent.
a.216
b.729
c.6! × 3!
d.None of the above
Q.5 The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is:
a.D(15)
b.15!
c.30C15
d.30P15
Q.6 Five students are to be arranged on five chairs for a photograph. Three of these are girls and the rest are boys. Find the total number of arrangements, in which three girls are together.
a.36
b.120
c.12
d.None of the above
Q.7 From a group of 5 men and 10 women, a committee has to formed of 5 members in which at least 4 men are required. The committee can be formed in .................... ways.
a.50
b.15C5
c.51
d.None of the above
Q.8 5 Indian and 5 American couples meet at a party and shake hands. If no wife shakes hands with her husband and no Indian wife shakes hands with a male, then find the number of hand shakes that take place in the party?
a.120
b.240
c.480
d.None of the above
Q.9 A shop owner has an unlimited supply of 8 different types of flowers. If a customer asks for a five flower arrangement such that the arrangement should start and end with the same type of flower, then in how many ways the arrangement can be made by the shop owner?
a.8C4 x 3!
b.83
c.84
d.8C4 x 4C1 x 3!
Q.10 In how many ways can be select 5 cards from a card pack such that all 4 suits appear?
a.52728
b.405646
c.685464
d.4056
Q.11 In a chess tournament, all participants were to play one game with the other. Two players fell ill after having played 3 games each. If total number of games played in the tournament is equal to 84, then total number of participants in the beginning was equal to:
a.14
b.15
c.16
d.18
Q.12 There is a straight table with a capacity of 9 members and they have to sit only on one side of the table. Arrange 4 boys and 5 girls such that the boy must have two girls adjacent to the boy (on either side). Find the total number of arrangements.
a.1840
b.2160
c.2880
d.6240
Q.13 The number of ways in which a mixed double game can be arranged from amongst 9 married couples, if no husband and wife play in the same game is:
a.1512
b.1514
c.3024
d.3028
Q.14 From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is:
a.At least 750 but less than 1000
b.At least 1000
c.Less than 500
d.At least 500 but less than 750
Q.15 A box contains 4 different pink balls and 5 different blue balls. In how many ways can you make a selection so as to take at least 1 pink ball and 1 blue ball?
a.(24 - 1) × (25 - 1)
b.(29 - 1)
c.(9! - 1)
d.None of the above
Q.16 In how many ways can a committee of 5 persons be formed from 6 gents and 4 ladies so that there is at least one lady in the committee?
a.246
b.10C5
c.10P5
d.None of the above
Q.17 There are 280 ways of forming a group of (x + 2) men and 3 women out of a total of 8 men and 5 women. Find the value of x.
a.2
b.3
c.4
d.6
Q.18 Three men have 4 coats, 5 waist coats and 6 caps. The number of ways they can wear them is:
a.15P3
b.4C3 × 5C3 × 6C3
c.180
d.4P3 × 5P3 × 6P3
Q.19 An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that atmost three of them are red is .................... .
a.420
b.455
c.490
d.None of these
Q.20 Kavita has 10 friends and she wants to invite 6 of them to a party. How many times will 3 particular friends always attend the party?
a.10C6
b.10C3
c.7C3
d.None of the above
Q.21 A double-decker bus has 5 empty seats in the up-stair and 5 empty seats in the down stair. 10 people board the bus of which 2 are old people and 3 are children. The children refuse to take seats down stair while old people insist to stay down-stair. In how many different arrangements can be 10 people take their seats in the bus?
a.144000
b.146000
c.146400
d.None of these
Q.22 The number of ways in which 3 distinct numbers in AP can be selected from 1, 2, 3, ….24 is
a.132
b.572
c.264
d.150
Q.23 The number of ways of arranging 7 persons (A, B, C and D among them), in a row so that, A, B, C and D are always in the order A – B - C- D (not necessarily together) will be
a.24
b.5040
c.210
d.None of the above
Q.24 The number of ways of dividing 10 books into 3 group of 5,3,2, books respectively is
a.10C5 . 5C3 . 2C2
b.10C5
c.10!
d.None of the above
Q25Find the number of ways of dividing 12 people among three groups such that one group has 6 members and each of the other two groups has 3 members
a.12C6
b.12P6
c.12C6 . 6C3. 3C
d.12C6 . 6C3. 3C3 / 2!
Answer for Permutation and Combination for CAT
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
A | A | B | B | B | A | C | D | C | C |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
B | C | A | B | A | A | C | D | C | C |
21 | 22 | 23 | 24 | 25 | |||||
A | A | C | A | D |
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