Permutation and Combination Questions for CAT 2026 — Words and Alphabets with Solutions
- Jul 22, 2025
- 4 min read
Updated: 5 days ago
PERMUTAION AND COMBINATION Question for CAT
Q.1 In how many different ways can the letters of the word TABLE' be arranged?
a.45
b.60
c.90
d.120
Q.2 In how many different ways can the letter of the word 'BELIEVE' be arranged?
a.840
b.5040
c.40320
d.None of the above
Q.3 In how many different ways can the letters of the word ‘SUBJECTION’ be arranged so that all the vowels always come together?
a.10!
b.7! × 4!
c.6! × 4!
d.None of the above
Q.4 In how many different ways can the letters of the word ‘BOOKKEEPER’ be arranged?
a.10! / (2! × 2! × 3!)
b.10! / 7!
c.10!
d.None of the above
Q.5 In how many different ways can the letters of the word ‘LONGEST’ be arranged so that the vowels are at the two ends?
a.7!
b.5!
c.5! × 2!
d.None of the above
Q.6 In how many different ways can the letters of the word ‘FINDER’ be arranged so that the vowels are never together?
a.6! – (5! × 2!)
b.6! / 2!
c.6! – (4! × 2!)
d.None of the above
Q.7 In how many different ways can the letters of the word ‘ACTION’ be arranged so that the vowels occupy only the odd positions?
a.6!
b.3! × 3!
c.6! / 2!
d.None of the above
Q.8 How many 5-letter words (with or without meaning) can be formed out of the letters of the word, ‘DIRECTLY’, if repetition of letters is not allowed?
a.8C5
b.8P5
c.5!
d.8!
Q.9 In how many ways can letters the word 'ATTITUDE' be arranged such that no two Ts are adjacent to each other?
a.6720
b.2400
c.4320
d.1800
Q.10 How many 6 letter words can be formed from the letters of the word “SPECTRUM” so that S and M occupies the first and last position respectively and repetition of the letters is allowed?
a.1296
b.4096
c.8192
d.360
Q.11 In how many ways can we arrange the letters of the word 'MANANA' such that no two A’s are adjacent to each other?
a.3! × 5C3
b.4! × 4C3
c.3 × 4C3
d.3! × 4C3
Q.12 How many ways are there for arranging letters of the word 'AMAZING' such that the ‘I’ appears between the two ‘A’s?
a.120
b.240
c.720
d.840
Q.13 Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
a.5!
b.7C3 × 4C2 × 5!
c.11C5
d.11P5
Q.14 In a word, there are 6 consonants and 4 vowels. In how many ways can we form a 4-letter word having two consonants and two vowels?
a.2160
b.5040
c.10C4
d.None of the above
Q.15 If letters of the word ‘KUBER’ are written in all possible orders and arranged as in a dictionary, then rank of the word ‘KUBER’ will be:
a.48
b.49
c.66
d.67
Q.16 The letters of the word SURITI are written in all possible orders and these words are written out as in a dictionary. Then find the rank of the words SURITI.
a.233
b.234
c.235
d.236
Q.17 If the letters of the word “FATE” are arranged in a dictionary order without repetition, then the rank of the arrangement of “FAET” is
a.12
b.13
c.14
d.15
Q.18 How many words can be formed with the letters of the word 'PATALIPUTRA' without changing the relative order of the vowels and consonants?
a.3600
b.4200
c.54000
d.3000
Q.19 Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is
a.105- 10P5
b.10P5
c.10C5
d.105
Q.20 How many five letter words (with or without meaning) can be formed such that the letters appearing in the odd positions are taken from the unrepeated letters of the word MATHEMATICS whereas the letters which occupy even places are taken from amongst the repeated letters of the same?
a.3600
b.540
c.150
d.None of these
Answer for Permutation and Combination for CAT
Frequently Asked Questions — Permutation and Combination: Words and Alphabets for CAT 2026
How many words can be formed from n letters with all distinct letters?
From n distinct letters, the number of words of r letters (order matters) = nPr = n!/(n-r)!. For all n letters together = n!. If there are repeating letters, divide by the factorial of each repeat count.
What is the formula for words from letters with repetition?
If a word has n letters where one letter repeats p times, another q times, etc., total arrangements = n! / (p! x q! x ...). For example, MISSISSIPPI has 11 letters: M x1, I x4, S x4, P x2, so arrangements = 11!/(1! x 4! x 4! x 2!).
How do I count words starting or ending with a specific letter?
Fix the specific letter in the required position, then arrange the remaining (n-1) letters in the remaining positions. If the starting letter must be a vowel from 3 vowels among 6 letters: fix one of the 3 vowels, then arrange the rest in 5! ways.
What is the rank of a word in dictionary order?
To find the rank of a word: count all words that come before it alphabetically. For each position, count how many smaller letters can fill that spot times arrangements of remaining letters. Sum all these counts and add 1.
How do I count words where vowels are always together?
Treat all vowels as a single unit. If there are v vowels and c consonants, arrange (c+1) units in (c+1)! ways, then multiply by v! for the internal arrangements of vowels. If vowels have repetitions, divide accordingly.
What is the difference between permutation of words and selection of letters?
Permutation (arrangement) counts ordered sequences. Combination (selection) counts unordered subsets. Word problems are permutation problems; committee-type problems are combination problems.
How many words can be formed from ARRANGEMENT using its letters?
ARRANGEMENT has 11 letters: A(2), R(2), N(2), G(1), E(2), T(1), M(1). Total arrangements = 11! / (2! x 2! x 2! x 2!) = 2,494,800.
How should I practice word-arrangement problems for CAT?
Start with 4-5 letter words with distinct letters, then progress to words with repeating letters, then constrained problems (vowels together, consonants together, specific positions). Practice 5 problems daily for 2 weeks.
Question 3's correct answer should be option b)