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How do I solve the following problem?How many ways can a football team of 9 be arranged...

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catd1115 | Middle School Teacher | (Level 3) Assistant Educator

Posted August 16, 2011 at 11:08 AM via web

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How do I solve the following problem?

How many ways can a football team of 9 be arranged if the kicker must be in the middle?

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted August 16, 2011 at 12:41 PM (Answer #1)

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Here is a visual way to do it.  Imagine each blank is a player's position:

___  ___  ___  ___  kicker  ___  ___  ___  ___

The kicker position is taken, the other 8 can fit into the other spaces.

8 * 7 * 6 * 5 * 1(kicker) * 4 * 3 * 2 * 1 = 40,320 arrangements

Another way to do this is using a permutation - an ordered arrangement in which no objects can be repeated.

Use a permutation of 8 instead of 9 because the kicker position is already taken.

8! = 40,320 arrangements

 

 

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