SOLUTION: an advertising artist has eight photographs from which to choose in designing a full page magazine ad containing 3 photographs. the position on the page is immaterial. how many des

Question 1029486: an advertising artist has eight photographs from which to choose in designing a full page magazine ad containing 3 photographs. the position on the page is immaterial. how many designs using different combinations of photographs are possible. show working please.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
an advertising artist has eight photographs from which to choose in designing a full page magazine ad containing 3 photographs. the position on the page is immaterial. how many designs using different combinations of photographs are possible. show working please.

Short answer:
8 choose 3 = C(8,3) = 8!/(3!(8-3)!)=8*7*6/(1*2*3)=56

Detailed answer:
Put a page in front of you and choose the first picture out of 8, so 8 choices.
There are 7 choices for the second picture and 6 for the third.
In total, there are 8*7*6=336 ways to choose three pictures out of 8.
However, the three pictures could have been chosen in 3!=6 different ways
(ABC, ACB, BAC, BCA, CAB, CBA) so we have to reduce the 336 ways by 6 = 56 ways as before.
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