how many positive integers less than 9999 are such that the product of their digits is 210.
Pick one:
A) 24  B) 58  C) 26  D) 34  E) 25
The prime factorization of 210 is 2*3*5*7. So one way to make the right kind of number is to use those four digits, in any of the 4! = 24 orders you can put them in.   Notice though that we can also get 210 as a product by multiplying 5, 6 and 7. So we can make some 3-digit numbers with the right product: 3! = 6 of them to be exact.   But we can also get the right product using the digit 1 along with the digits 5, 6, and 7. Again we can arrange those digits in 4! = 24 orders.   24
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how many positive integers less than 9999 are such that the product of their digits is 210.