6 sopranos and 8 baritones. In how many ways can the director choose a quartet (4 people) that contains at least one soprano? I'm using a TI-83, so if you can give me the steps that would be great. Thanks
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I know nothing about your TI-83, sorry ...
There are 6 sopranos and 8 baritones, or 14 people altogether
Two ways to approach it are:
1) Find the total number of quartets (TNOQ) for 14 singers, find the TNOQ with 4 baritones, and subtract.
2) Find the TNOQ with 1 soprano, then the TNOQ with 2 sopranos, then the TNOQ with 3 sopranos, then add.
The 2nd way is more boring and the 1st way is more clever, so do that.
The selection is done "without replacement" (I never bother to think that, but it might help if you look it up.)
The function to use is "combinations".
(14 choose 4) - (8 choose 4)
This can be computed by the Google engine's search tools
(14 choose 4) - (8 choose 4) = 931
http://www.google.com/search?q=+(14+choo…
There are 6 sopranos and 8 baritones, or 14 people altogether
Two ways to approach it are:
1) Find the total number of quartets (TNOQ) for 14 singers, find the TNOQ with 4 baritones, and subtract.
2) Find the TNOQ with 1 soprano, then the TNOQ with 2 sopranos, then the TNOQ with 3 sopranos, then add.
The 2nd way is more boring and the 1st way is more clever, so do that.
The selection is done "without replacement" (I never bother to think that, but it might help if you look it up.)
The function to use is "combinations".
(14 choose 4) - (8 choose 4)
This can be computed by the Google engine's search tools
(14 choose 4) - (8 choose 4) = 931
http://www.google.com/search?q=+(14+choo…