JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Permutations and Combinations

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Let P be the set of seven digit numbers with sum of their digits equal to 11 . If the numbers in P are formed by using the digits 1,2 and 3 only, then the number of elements in the set P is :
  1. (A)158
  2. (B)173
  3. (C)164
  4. (D)161✓ Correct

Answer: (D)

Solution

Let a 7-digit number use ones, twos and threes, so


Subtracting, , giving three integer solutions:

: digits , arrangements .

: digits , arrangements .

: digits , arrangements .

Total: .

JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Single correct option

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