MHB -aux.14.12 boys and 10 girls randomly selected

[karush]

2000
Of 12 boys and 10 girls, a teacher randomly selects 2 boys and 2 girls to be crossing guards, how many outcomes are there to this process?
Tried to the fundamental counting principal on this but
$10\cdot10\cdot12\cdot12=14400$

Bk says its 2970?

 

[soroban]

Hello, karush!

Of 12 boys and 10 girls, a teacher randomly selects 2 boys and 2 girls
How many outcomes are there to this process?

Select 2 boys from 12 boys.
\qquad There are: \:_{12}C_2 \,=\,{12\choose2}\,=\,\frac{12!}{2!\,10!} \,=\,66 ways.

Select 2 girls from 10 girls.
\qquad There are: \:_{10}C_2 \,=\,{10\choose2} \,=\,\frac{10!}{2!\,8!} \,=\,45 ways.

Therefore, there are: \:66\cdot45 \:=\:2970 outcomes.

 

[karush]

Think I got it using combinations

$\frac{10!}{(10-2)!2!}\cdot\frac{12!}{\left(12-2\right)!2!}=2970$