Mathematics · Permutations and Combinations

JEE Main 2025 — 2 April, Morning Shift — Question 32

The number of sequences of ten terms, whose terms are either $0$ or $1$ or $2 ,$ that contain exactly five $1$ s and exactly three $2$ s , is equal to:

Option A:
$1820$
Option B:
$2520$
Correct
Option C:
$360$
Option D:
$45$

Answer: B

Step-by-step solution

Exactly five 1 s and exactly three 2 s

$\Rightarrow 2$ zeros must be used

$\Rightarrow 10$ places to arrange 5 ones, 3 twos and 2 zeros

$\Rightarrow \frac{10!}{2!3!5!}=2520$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 2 April, Morning Shift
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Problems based on both permutations and combinations

The largest n in N such that 3^n divides 50 ! Is

Answer: B

Step-by-step solution

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