15 people apply for a job to be a trainee. Only 5 can be picked. In how many ways can a group of 5 trainees be picked?

1 Answer
MathFact-orials.blogspot.com
Oct 23, 2016

3003

Explanation:

This is a Combinations question (picking Trainee 1, 2, 3, 4, 5 is the same as picking Trainee 5, 4, 3, 2, 1) so we can express this as:

#C_(15,5)=(15!)/((10!)(5!))=(15xx14xx13xx12xx11xx10!)/((10!)(5xx4xx3xx2xx1))#

And now let's simplify:

#(color(orange)(cancel(15))xxcolor(blue)(cancel(14))^7xx13xxcolor(green)(cancel(12))^3xx11xxcolor(red)(cancel(10!)))/(color(red)(cancel((10!)))(color(orange)(cancel(5))xxcolor(green)(cancel(4))xxcolor(orange)cancel(3)xxcolor(blue)(cancel(2))xx1))#

#7xx13xx3xx11=3003#

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