SOLUTION: In how many ways can a selection of at least two CDs be made from a set of 7 CDs

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Question 1137970: In how many ways can a selection of at least two CDs be made from a set of 7 CDs
Found 3 solutions by Boreal, greenestamps, Edwin McCravy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
This is 7C2=21
It is 7!/2!*5!
=7*6/2*1
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Choosing at least 2 of the 7 CDs means you are NOT choosing either 0 or 1 of them.

The total number of possible selections of any number of the CD's is 2^7 = 128.

There is obviously only 1 way to choose 0 of the CD's, and there are 7 ways to choose 1 of them.

So the number of ways of choosing at least 2 of the 7 CD's is 128-(1+7) = 120.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
For each of the 7 CD's, you have exactly 2 decisions to make:
(1) Choose it!
or
(2) Don't choose it!

So there are 2×2×2×2×2×2×2 = 27 = 128 ways to make a decision for
each CD, to choose or not choose it.  However, from that 128 we need to
subtract:

(a) The 7 ways we could choose only 1 CD.
and
(b) The 1 way we could have chosen no CDs at all, which case is included in
    the 128 as the one case where "(2) Don't choose it!" was decided for
    every CD.

So the final answer is 128-7-1 = 120 ways.

Edwin
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