Combinations and selections - S1 Maths A-level Watch

nonipaify
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A chois consists of 13 sopranos 12 altos 6 tenors and 7 bases. A group consisting of 10 sopranos 9 altos 4 tenors and 4 bases is to be chosen from the choir. In hiw many different ways can the group be chosen?

Now I know this is a simple selection 13c10 12c9 6c4 7c4... but why are the results multiplied instead of being added?
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ghostwalker
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(Original post by nonipaify)
A chois consists of 13 sopranos 12 altos 6 tenors and 7 bases. A group consisting of 10 sopranos 9 altos 4 tenors and 4 bases is to be chosen from the choir. In hiw many different ways can the group be chosen?

Now I know this is a simple selection 13c10 12c9 6c4 7c4... but why are the results multiplied instead of being added?
Consider one combination of altos, tenors and bases. For this combination you could have any of the 13c10 choices of sopranos. Since this is true for any other combination of altos, tenors, and bases, then it's 13C10 times .... Similarly the others.

If it's still confusing you might find it useful to use a simpler example and end list all the combinations.

Say, 3 sopranos {A,B,C}, 2 altos {R,S}, and 2 bases {X,Y} and you want to choose 1 of each.
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