CA Foundation · Quantitative Aptitude · Permutations and Combinations
In a library, there are 5 identical English books, 4 identical Hindi books, and 3 identical Sanskrit books. In how many ways can these books be arranged in a row on a shelf?
With 12 total books where 5 are identical English, 4 identical Hindi, and 3 identical Sanskrit, the arrangements are 12! / (5! × 4! × 3!) = 27,720.
- A27720Correct
- B60480
- C5040
- D18900
Explanation
This is a permutation with identical objects. Total books = 5 + 4 + 3 = 12. The formula is n! / (n₁! × n₂! × n₃!) where n₁=5, n₂=4, n₃=3. So we get 12! / (5! × 4! × 3!) = 479001600 / (120 × 24 × 6) = 479001600 / 17280 = 27720. The distractor 60480 is 12!/(4!×3!), ignoring one repeated group. The distractor 5040 is 7!, and 18900 is an incomplete calculation.
Did you get it right without looking?
One question tells you little. A timed set on Permutations and Combinations shows your real accuracy, how long you take and where you lose marks.
More Permutations and Combinations questions
- How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6 where no digit is repeated?
- How many distinct arrangements of the letters of the word COMMITTEE are there in which all the vowels stay together?
- A committee of 3 members is to be chosen from 8 teachers at a school in Pune. In how many ways can this be done?
- How many distinct arrangements can be made using all the letters of the word 'BANANA' in which the letters are placed in a row?
- In how many ways can the letters of the word 'LOGIC' be arranged such that the vowels are always together?
- Six directors of a company in Pune are to be seated around a circular table for a board meeting. In how many distinct ways can they be seate…