Question

21 22 23 24 25 TIME REMAINING 01:40:27 A hat contains slips of paper with the names of the 26 other students in Eduardo’s class on them, 10 of whom are boys. To determine his partners for the group project, Eduardo has to pull two names out of the hat without replacing them. What is the probability that both of Eduardo’s partners for the group project will be girls?

Answer 1

There are 26 - 10 = 16 girls. The number of ways to choose 2 girls from a set of 16 is C(16, 2) = 120. (Your class might be using a different notation for combinations, like $_{16}C_2$.)

The number of ways to choose 2 people (boys or girls) from a set of 26 is C(26, 2) = 325.

The probability of choosing 2 girls is $\frac{120}{325} = \frac{24}{65}$

Example: how to compute C(16,2):

$C(n, r) = \frac{n!}{r!(n-r)!} \\ C(16, 2) = \frac{16!}{2!(16-2)!} \\ =\frac{16!}{2! \times 14!} \\ =\frac{16\times 15}{2\times 1} \\ =120$