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Mathematics · Permutations and Combinations

JEE Main 2024 — 1 February, Shift 1 — Question 5

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:

  1. Option A:

    47

  2. Option B:

    53

  3. Option C:

    51

    Correct
  4. Option D:

    43

Answer: C

Step-by-step solution

Total ways to partition 5 into 4 parts are : 5,0,0,0⇒15,0,0,0 \Rightarrow 1 way

4,1,0,0⇒5!4!=54,1,0,0 \Rightarrow \frac{5!}{4!}=5

ways 3,2,0,0,⇒5!3!2!=103,2,0,0, \Rightarrow \frac{5!}{3!2!}=10 ways

2,2,0,1⇒5!2!2!2!=152,2,0,1 \Rightarrow \frac{5!}{2!2!2!}=15

ways 2,1,1,1⇒5!2!(1!)33!=102,1,1,1 \Rightarrow \frac{5!}{2!(1!)^{3} 3!}=10 ways

3,1,1,0⇒5!3!2!=103,1,1,0 \Rightarrow \frac{5!}{3!2!}=10 ways

Total ⇒1+5+10+15+10+10=51\Rightarrow 1+5+10+15+10+10=51 ways

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
1 February, Shift 1
Subject
Mathematics
Chapter
Permutations and Combinations
Topic
Distribution of Objects into Groups

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