JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Permutations and Combinations

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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 ______.

Answer: 36

Solution

3-digit numbers from

{2, 3, 4, 5, 7}

(no repetition) not divisible by 3. A number is divisible by 3 iff its digit sum is. Among the digits, the triples whose sum is a multiple of 3 are those to EXCLUDE; the remaining valid digit-triples number 6, and each arranges in

3! = 6

ways. Total

= 6 \times 6 = 36

JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Integer answer

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