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Solution


Q.

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5, and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to _______.           [2024]

Ans.

(36)

Possible triplets for which number is divisible by 3 are (2, 3, 4), (2, 3, 7), (3, 5, 4), (3, 5, 7)

These 4 triplets can be arrange in 4×3!.

Total number of 3-digit numbers made by using the digits 2, 3, 4, 5, and 7 =C3×3!5

Required number which are not divisible by 3 =C3×3!-4×3!=6×3!=365