Digit Product of 10000 (from Brilliant.org) How many 7 digit positive integers are there such that the product of the individual digits of each number is equal to 10000?
Details and assumptions
As an example, 22225555 is an 8 digit integer, whose product of individual digits is 10000.
Note: This is a past question from brilliant.org.

$10000=2^45^4$
You need $7$ digits, so only possibility for digits are $(4,2,2,5,5,5,5),(4,4,1,5,5,5,5),(8,2,1,5,5,5,5)$
Now, no. of permutation of this set of digits gives you the required answer = $\frac{7!}{2!4!}+\frac{7!}{2!4!}+\frac{7!}{4!}$
