Multiple choice general knowledge

Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?

  1. 144

  2. 168

  3. 192

  4. none
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C Correct answer
Explanation

For a number to be divisible by 4, its last two digits must be divisible by 4. From {1,2,3,4,5,6}, the pairs divisible by 4 are: 12, 16, 24, 32, 36, 52, 56, 64 (8 pairs). For each pair, we need to fill the first 3 positions from remaining 4 digits. Number of ways = 4P3 = 4 × 3 × 2 = 24. Total = 8 × 24 = 192.

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