Question

If 5 cars are selected from 8 and arranged side-by-side in a parking lot, how many permutations are

possible?

Answer 1

Answer: 6720

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Step-by-step explanation:

We have five slots which we can label A,B,C,D,E

• There are 8 choices for slot A
• Then 7 choices for B
• 6 for C
• 5 for D
• 4 for E

We start at 8 and count down by 1 each time until all slots are accounted for. Then multiply out those items: 8*7*6*5*4 = 6720

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Another approach is to use the nPr permutation formula.

Plug in n = 8 and r = 5.

`n P r = (n!)/( (n-r)! )\\\\8 P 5 = (8!)/( (8-5)! )\\\\8 P 5 = (8!)/( 3! )\\\\8 P 5 = (8*7*6*5*4*3!)/( 3! )\\\\8 P 5 = 8*7*6*5*4\\\\8 P 5 = 6720\\\\`

In the second to last line, the "3!" factorial terms cancel out.

We have the string 8*7*6*5*4 show up again to help reinforce the previous section.