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How many positive integers can be expressed as a product of

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Manager
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Joined: 28 Apr 2003
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How many positive integers can be expressed as a product of [#permalink] New post 06 Dec 2003, 21:56
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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. 8
b. 9
c. 10
d. 11
e. 12


I could only get the below workings, and I am not sure if someone can provide a shortcut way to derive it.

5x7
5x11
5x13
7x11
7x13
11x13
Director
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 [#permalink] New post 06 Dec 2003, 22:01
Quote:
How many positive integers can be expressed as a product
of two or more of the prime numbers
(emphasis mine)

As you have discovered, there are 6 (4 choose 2) pairs.
You have neglected sets of three (4 choose 3) 4
and the set of four 1

6+4+1=11
Manager
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 [#permalink] New post 06 Dec 2003, 22:14
So the remaining answers are:

5x7x11
5x7x13
5x11x13
7x11x13
5x7x11x13
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 [#permalink] New post 09 Dec 2003, 04:06
guys, learn to apply combinatorics: 4C2+4C3+4C4=6+4+1=11
  [#permalink] 09 Dec 2003, 04:06
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How many positive integers can be expressed as a product of

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