VandyonWheels wrote:

In how many ways can 3 people out of 14 people be given 3 prizes(gold,silver,bronze) so that Jack is awarded? Jack is one of 14 people.

The given answer is

but I have not been able to understand how.

The direction that I proceeded was:

Jack gets gold or jack gets silver or jack gets bronze

=\(13*12 + 13*12 + 13*12\)

This seems to be wrong,so if somebody could explain where I'm going wrong and how to arrive at the correct answer it would be great!

Please help!

Lets ensure Jack gets a prize - 1C1

Choose any 2 from the remaining 13 get prizes - 13C2

Ways of distributing 3 prizes among 3 people - 3!

So total number of ways - \(1C1 * 13C2 * 3!\) = \(1*13*6*6\) = \(468\)