10 people can line up in (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2) = 3,628,800 different ways.
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10!, which is pronounced "10 factorial". This is calculated as 1 x 2 x 3 x 4 ... x 10.
First in line can be any of the 12, second can be any of the remaining 11, third any of 10 and fourth any of 9 so 12 x 11 x 10 x 9 ie 11880 different ways
Assuming the Ps and Is are indistinguishable: There are 10! / 3! / 3! = 100800 ways If the Ps and Is are distinguishable, then there are 10! = 3628800 ways
10
There are 13 ways.