danjuma wrote:How many positive integers less than 10,000 are such that the product of their digits is 210?

Sorry, i do not have the answer choice

For the product to be 210, we need exactly 3 * 7 * 2 * 5 .

There can be only be one combination 3 digit number is there 6 * 7 * 5 = Can be arranged in !3 ways , in total 6 numbers.

In 4 digit numbers be can include 1 as well.

Possible digits can be 1, 6 , 7 , 5 and 2 , 3 , 7 , 5 in total !4 * 2 = 48 such possible numbers are possible.

48 + 6 = 54 numbers are there.