JEE MAIN - Mathematics (2022 - 26th July Morning Shift - No. 16)

The number of 5-digit natural numbers, such that the product of their digits is 36 , is __________.
Answer
180

Explanation

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

$${{5!} \over {2!2!}} + {{5!} \over {2!2!}} + {{5!} \over {2!2!}} + {{5!} \over {3!}} + {{5!} \over {2!}} + {{5!} \over {3!2!}}$$

$$ = (30 \times 3) + 20 + 60 + 10 = 180$$.

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