1) How many ways can six books be arranged on one shelf?
2)There are eight girls competing in an ice-skating competition. In how many ways can they finish in first, second, and third place?
3)How many ways can a president and vice president be selected from a class of 12?
4)How many ways can seven students line up for a class picture?
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all of these use the counting principle
if there are n ways to do one thing and m ways to do another, there are \(n\times m\) ways to do them together
There are eight girls competing in an ice-skating competition. In how many ways can they finish in first, second, and third place?
8 choices for first
7 choices for second (since first is now taken)
6 choices for third
counting principle says it is \(8\times 7\times 6\)