Let's start by breaking 210 down into primes:hansoo wrote:How many positive integers less than 10,000 are such that the product of their digits is 210?
a) 24
b) 30
c) 48
d) 54
e) 72
210 = 10 * 21 = 2*5*3*7
So, to start, we know that all permutation of 2,3,5,7 will fulfil the requirements: 4! = 4*3*2 = 24
However, we have to recognize that we may be able to use 1 and another number in place of a pair of our numbers.
Since each digit has to be less than or equal to 9, the only substitution we can do is to use 1*6 instead of 2*3 (2*5, the next smallest pair of primes, would give us 10).
So, we can also use the digits 1,5,6,7. Same as last time, this gives us 4! = 24 possible arrangements.
So, the final answer is 24+24=48... choose C
