# Pairs

From the five girls and four boys teachers have to choose one pair of boy and girl.

A) How many such pairs of (M + F)?
B) How many pairs where only boys (M + M)?
C) How many are all possible pairs?

Correct result:

a =  20
b =  6
c =  36

#### Solution:

$a=4 \cdot \ 5=20$
$b=4 \cdot \ 3 / 2=6$
$C_{{ 2}}(9) = \dbinom{ 9}{ 2} = \dfrac{ 9! }{ 2!(9-2)!} = \dfrac{ 9 \cdot 8 } { 2 \cdot 1 } = 36 \ \\ c={ { 2 } \choose 5+4 }=36$

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