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:

$a=4\cdot 5=20$

$b=4\cdot 3\mathrm{/}2=6$

$$\begin{gathered} C_2(9)=\left({\displaystyle \genfrac{}{}{0px}{}{9}{2}}\right)={\displaystyle \frac{9!}{2!(9-2)!}}={\displaystyle \frac{9\cdot 8}{2\cdot 1}}=36 \\ c=\left(\genfrac{}{}{0px}{}{2}{5+4}\right)=36 \end{gathered}$$

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