Mathematics · Permutations and Combinations

JEE Advanced 2018 — Paper 1 — Question 34

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 $\qquad$ .

Answer: 625

Numerical answer — enter this value.

Step-by-step solution

For a number to be divisible by 4, the last two digits must form a number divisible by 4. From the given digits $\{1,2,3,4,5\}$ , the two-digit numbers divisible by 4 are $12, 24, 32, 44, 52$ .

So there are 5 possible endings. The first three digits can be any of the 5 digits with repetition, so there are $5 \times 5 \times 5 = 5^3 = 125$ choices. By the fundamental principle of counting, total numbers $= 125 \times 5 = 625$ . Thus, the answer is 625.

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2018
Paper: Paper 1
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Number of integral divisors of number