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John wants to choose 4 of his friends to go to Disneyland with him. If he has 15 friends, in howmany ways can he choose 4 of them?

John wants to choose 4 of his friends to go to Disneyland with him. If he has 15 friends-example-1
User HashDefine
by
6.7k points

1 Answer

6 votes

In this case, the order does not matter and we can not replace it.

Hence, we need to use a combination for this case.

The equation is given by:


nCx=(n!)/(x!(x-n)!)

Where n represents the total number of friends and x represents the number of the group.

Then,

n = 15 friends

x = choose 4 of them

Replacing:


15C4=(15!)/(4!(15-4)!)

Simplify:


\begin{gathered} 15C4=(15!)/(4!11!) \\ 15C4=1365 \end{gathered}

Hence, Jhon can choose them 1365 ways.

The correct answer is option d.

User Aboodrak
by
6.7k points
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