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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