Question

How many ways can 12 swimmers finish in first second and third place?Permutation or Combination?

Answer 1

This is a permutation since order matters. A sequence like ABC is different from CBA.

There are 12 choices for the first slot, then 11 choices for the next, and 10 choices for the last slot.

There are 12*11*10 = 1320 different ways of having 1st, 2nd, and 3rd place.

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Another way to arrive at 1320 is to use the nPr formula where the input values are n = 12 and r = 3.

The nPr formula is
`_nP_r = (n!)/((n-r)!)`

The exclamation marks indicate factorials.

For example: 12! = 12*11*10*9*8*7*6*5*4*3*2*1 = 479,001,600