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43 votes
43 votes
There are 6 forwards and 4 guards on the Tigers girls basketball team. Coach Briggs will randomly choose two captains for the next game. What is the probability that both captains will be forwards?

User Chamil Kandamby
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1 Answer

18 votes
18 votes

(1)/(3)

1) Let's find the sample space, i.e. the number of the total outcomes (favorable and not favorable). Let's consider that we need to pick 2 out of ten, that is our sample space.


_(10)C_2=(10!)/(2!*8!)=45

2) Now, let's find the number of favorable events. In this case, both players must be a forward. The favorable event includes only forward players out of those 6:


_6C_2=(6!)/(2!(6-2)!)=15

3) We can write out the probability of picking one forward and another forward. Note that there was no replacement after each picking:


P=(15)/(45)=(1)/(3)

User Seddonym
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