How many 7 digit positive integers are there such that the product of the individual digits of each number is equal to 10000?

Answer 1

10000 = 10^4 = 2^4 * 5^4
so, the digits must be all 1's, 2's and 5's

Since you need all 8 2's and 5's to get 10,000, no 7-digit number will do it.

Answer 2

4455551 = 4x4x5x5x5x5x1=10000
the proof is not valid.