McGraw Hill Glencoe Algebra 2, 2012
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McGraw Hill Glencoe Algebra 2, 2012 View details
4. Counting Techniques
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Exercise 16 Page P12

Is the order important?

Permutations or combinations? Permutations
Answer: 840

Practice makes perfect

We want to find how many ways there are to choose 4 out of 7 different players. Note that, in this case, the order is important. Thus, each possible arrangement is a permutation. To calculate the answer, we will use the formula for permutations of n players taken r at a time. _n P_r = n!/(n-r)! We have 7 players and are taking 4 at a time. This means that n= 7 and r= 4. Let's substitute these values in the above formula.

_n P_r = n!/(n-r)!
_7 P_4 = 7!/( 7- 4)!
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Simplify
_7 P_4 = 7!/3!

Write as a product

_7 P_4 = 7* 6* 5* 4* 3!/3!
_7 P_4 = 7* 6* 5* 4/1
_7 P_4 = 840/1
_7 P_4 = 840

There are 840 permutations.