Mathematics · Permutations and Combinations

JEE Main 2026 — 2 April, Morning Shift — Question 25

The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is….

Option A:
15400
Option B:
17800
Option C:
16800
Correct
Option D:
29400

Answer: C

Step-by-step solution

Exactly one digit repeated $\rightarrow^{5} \mathrm{C}_{1} \times \frac{7!}{3!}=4200$ Exactly two digits repeated $\rightarrow{ }^{5} \mathrm{C}_{2} \times \frac{7!}{2!2!}=12600$

Total numbers $=16800$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 2 April, Morning Shift
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Problems based on both permutations and combinations