document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #644511 by mathmate(429) $\"\"$ $\"About$

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\n" ); document.write( "Question:
\n" ); document.write( "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.
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\n" ); document.write( "Short answer:
\n" ); document.write( "8 choose 3 = C(8,3) = 8!/(3!(8-3)!)=8*7*6/(1*2*3)=56
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\n" ); document.write( "Detailed answer:
\n" ); document.write( "Put a page in front of you and choose the first picture out of 8, so 8 choices.
\n" ); document.write( "There are 7 choices for the second picture and 6 for the third.
\n" ); document.write( "In total, there are 8*7*6=336 ways to choose three pictures out of 8.
\n" ); document.write( "However, the three pictures could have been chosen in 3!=6 different ways
\n" ); document.write( "(ABC, ACB, BAC, BCA, CAB, CBA) so we have to reduce the 336 ways by 6 = 56 ways as before. \n" ); document.write( "

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