JEE Main 2024MathematicsPermutation CombinationHardMCQ

JEE Main 2024 — Permutation Combination Question with Solution

JEE Main 2024 (01 Feb Shift 1)

Question

If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to:

Choose an option

Show full solutionCorrect option: C
Correct answer
C51

Step-by-step explanation

Given,

Rooms are identical,

So, total ways to distribute 5 employees into 4 rooms are:

5,0,0,0⇒1 way

4,1,0,0⇒5!4!=5 ways

3,2,0,0⇒5!3!2!=10 ways

2,2,0,1⇒5!2!2!2!=15 ways

2,1,1,1⇒5!2!1!33!=10 ways

3,1,1,0⇒5!3!2!=10 ways

Total ⇒1+5+10+15+10+10=51 ways

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About this question

This is a previous-year question from JEE Main 2024, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.