JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Permutations and Combinations

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The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is ____.

Answer: 625

Solution

A number is divisible by 4 if its last two digits form a number divisible by 4.

From the set {1,2,3,4,5}, the two-digit numbers divisible by 4 are: 12, 24, 32, 44, 52 (5 possibilities).

The first three digits can be any of the 5 digits:

5^{3} = 125

ways.

Total:

125 \times 5 = 625

JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Numerical answer

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