Help me understand this one, please from Powerprep

[tomintampa]

1) How many positive integers can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once?

A) eight B) nine C) ten D) eleven E) twelve

Answer is D

I have seen the mechanics on solving it but im not sure WHY, can someone help? Thank you.

[bkparikh]

This can be treated as a combination question. The order of the prime factors does not matter (ex. 5 * 7 is the same as 7 * 5). And we know that no positive integers will be duplicated because the product of prime factors is unique.

We are looking for 4C4 + 4C3 + 4C2.

That is, given 4 items how many ways can we group 4 into a group of 4 (4C4) + how many ways to group 4 into a group of 3 (4C3) + how many ways to group 4 into a group of 2 (4C2).

This way we are finding all the possible combinations of 2 or more prime factors without repeating any.

The formula for nCr is n!/((n-r)!r!)

4C4 = 1, nCn always equals 1
4C3 = 4
4C2 = 6

Sum = 11

[tomintampa]

Thank you a million

[abhishek_mumbai]

Great.. I solved exacltly same way.. The beauty of these questions is that they can be solved in many ways - a number system question by Combinations..
I like the question - It is tricky and GMAT type.

[audia8]

Did it in the same way. D)11