Question

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

Answer 1

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