Permutations & Combinations Questions with Solutions
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.
- Q21.
From a group of 7 men and 6 women, a committee of 5 persons with more males than females is to be formed. In how many ways can this be done?
A. 564B. 645C. 735D. 756mediumAsked in NIMCET 2017View solution āŗ - Q22.
9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into the 3 small boxes. The number of ways of arranging one ball in each of the boxes is
A. 18720B. 18270C. 17280D. 17780mediumAsked in NIMCET 2018View solution āŗ - Q23.
How many natural numbers smaller than can be formed using the digits 1 and 2 only?
A. 786B. 666C. 766D. 10666mediumAsked in NIMCET 2018View solution āŗ - Q24.
Let n be the number of different 5-digit numbers, divisible by 4, that can be formed with the digits 1, 2, 3, 4, 5 and 6, with no digit being repeated. What is the value of n?
A. 144B. 168C. 192D. 222mediumAsked in NIMCET 2018View solution āŗ - Q25.
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in an English dictionary, then the position of the word QUEEN is
A. 47thB. 44thC. 45thD. 46thmediumAsked in NIMCET 2019View solution āŗ - Q26.
In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Also, the total number of games played by the men among themselves exceeded by 66 the number of games that the men played against the women. Then the total number of players in the tournament is
A. 13B. 11C. 9D. 7mediumAsked in NIMCET 2019View solution āŗ - Q27.
There are 9 bottles labelled 1, 2, 3, ..., 9 and 9 boxes labelled 1, 2, 3, ..., 9. The number of ways one can put these bottles in the boxes so that each box gets one bottle and exactly 5 bottles go in their corresponding numbered boxes is
A. B. C. D.mediumAsked in NIMCET 2024View solution āŗ - Q28.
Lines are distinct, among which the lines are parallel to each other and the lines pass through a given point C. The number of points of intersection of pairs of lines from the complete set is
A. 24B. 25C. 26D. 27mediumAsked in NIMCET 2024View solution āŗ - Q29.
The number of 3-digit integers that are multiples of 6 which can be formed by using the digits 1, 2, 3, 4, 5, 6 without repetition is
A. 22B. 20C. 26D. 24mediumAsked in NIMCET 2025View solution āŗ