In how many ways can three different awards be distributed among the 17 people in our school, if a.) No student may receive more than one award? B) there is no limit on the number of awards won by...

In how many ways can three different awards be distributed among the 17 people in our school, if

a.) No student may receive more than one award?

B) there is no limit on the number of awards won by one student?

 

Explain please

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a) You need to use the formula for the number of ways of choosing r items/people from n items/people

`C(n,r) = (n!)/(r!(n-r)!)`

We say 'n choose r'

Here `n=17` and `r=3` so the number of ways is

`C(17,3) = (17!)/(3!14!) = (17.16.15.14.13...3.2.1)/((3.2.1)(14.13.12...3.2.1))=(17.16.15)/(3.2.1)`

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