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JEE Main 2026 · 2 Apr · Shift 1, Mathematics question 6

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 :

Choose one option
Answer and worked solution

Official answer: C

Distribute 7 places among 5 digits, each used at least once. Two extra uses remain:

  • one digit used 3 times: 5×7!3!=42005\times\dfrac{7!}{3!}=4200;
  • two digits used twice each: (52)7!2! 2!=12600\binom52\dfrac{7!}{2!\,2!}=12600.

Total 1680016800.

(C)

Topics:Distribution and arrangements
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