Question 899713:
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website! How many committees of 1,2,3,4,5,6,7, or 8 members can be taken
from 8 section presidents in a certain college?
Suppose the 8 section presidents are A,B,C,D,E,F,G, and H
When choosing members for the committee,
there are 2 choices to make about A. They are:
1. choose A to be in the committee. 2. exclude A from the committee,
That's 2 choices we can make for A.
there are 2 choices to make about B. They are:
1. choose B to be in the committee. 2. exclude B from the committee,
That's 2*2 or 22 = 4 choices we can make for A and B.
there are 2 choices to make about C. They are:
1. choose C to be in the committee. 2. exclude C from the committee,
That's 2*2*2 or 23 = 8 choices we can make for A,B, or C.
...
there are 2 choices to make about H. They are:
1. choose H to be in the committee, 2. exclude H from the committee,
That's 2*2*2*2*2*2*2 or 28 = 256 choices we can make for
A,B,C,D,E,F,G, and H.
However, from the 256 we must subtract 1 way and that is the one way
in which we exclude all 8, for there would be no committee!
Answer: 256-1 = 265 ways to choose a committee.
Edwuin
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