Permutations & Combinations Questions with Solutions

63 questions29 easy29 medium5 hard

Permutations count arrangements where order matters, while combinations count selections where order does not matter. This topic covers the fundamental principle of counting, factorials, nPr and nCr, arrangements of letters in a word (including repeated letters), circular arrangements, and selecting committees or teams with conditions. The hardest part is deciding whether a question needs a permutation or a combination. Ask yourself whether swapping two chosen items gives a new outcome. If it does, order matters. Conditions such as "two people must sit together" are handled by treating them as a single unit, and "at least one" questions are usually easiest to solve as total minus none. Practise the permutation and combination questions below, each with a step-by-step solution showing how to set up the count.

All Questions Easy Medium Hard

Q21.
There are 8 students appearing in an examination of which 3 have to appear in Mathematics paper and the remaining 5 in different subjects. Then, the number of ways they can be made to sit in a row, if the candidates in Mathematics cannot sit next to each other is
A. 2400B. 16200C. 4200D. 14400
easyAsked in NIMCET 2014View solution ›
Q22.
If $42 \cdot ^{n} P_{2} = ^{n} P_{4}$ , then the value of $n$ is
A. 2B. 4C. 9D. 42
easyAsked in NIMCET 2015View solution ›
Q23.
How many 3-digit numbers divisible by 5 can be formed using the digits 2, 3, 5, 6, 7 and 9, without repetition of digits?
A. 216B. 20C. 120D. 24
easyAsked in NIMCET 2015View solution ›
Q24.
A student council has 10 members. From these, one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways can this be done?
A. 151200B. 75600C. 37800D. 18900
easyAsked in NIMCET 2018View solution ›
Q25.
Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?
A. 495B. 550C. 1045D. 2475
easyAsked in NIMCET 2019View solution ›
Q26.
How many 4-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5, if none of the digits is repeated?
A. 216B. 60C. 24D. 25
easyAsked in NIMCET 2019View solution ›
Q27.
The value of $\sum_{r = 1}^{n} \frac{ ^{n} P _{r}}{r !}$ is
A. $2^{n}$ B. $1 - 2^{- n}$ C. $2^{n} - 1$ D. $2^{2 n} - 1$
easyAsked in NIMCET 2024View solution ›
Q28.
Number of permutations of the letters of the word BANGLORE such that the string ANGLE appears together in all permutations, is
A. 120B. 24C. 720D. 1228
easyAsked in NIMCET 2025View solution ›
Q29.
Number of three-digit numbers that can be formed using 0, 1, 2, 3 and 5, where these digits are allowed to repeat any number of times, is equal to
A. 115B. 100C. 125D. 140
easyAsked in NIMCET 2025View solution ›

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