Question

The number of 5-digit natural numbers, such that the product of their digits is 36, is _____ .

Answer 1

Correct Answer: 180

The correct answer is 180
Factors of 36 = 2²⋅ 3²⋅ 1
Five-digit combinations can be
(1, 2, 2, 3, 3) (1, 4, 3, 3, 1), (1, 9, 2, 2, 1)
(1, 4, 9, 11) (1, 2, 3, 6, 1) (1, 6, 6, 1, 1)
i.e., total numbers
\(\frac{5!}{2!2!} + \frac{5!}{2!2!} + \frac{5!}{2!2!} + \frac{5!}{3!} + \frac{5!}{2!} + \frac{5!}{3!2!}\)
= (30 × 3) + 20 + 60 + 10 = 180