Question

Bob is planning to pack 6 shirts and 4 pairs of pants for a trip. If he has 10 shirts and 10 pairs of pants to choose from, in how many different ways can this be done?

Answer 1

$\displaystyle \binom{10}{6}\cdot\binom{10}{4}=\dfrac{10!}{6!4!}\cdot\dfrac{10!}{4!6!}=\dfrac{7\cdot8\cdot9\cdot10}{2\cdot3\cdot4}\cdot\dfrac{7\cdot8\cdot9\cdot10}{2\cdot3\cdot4}=\\ =210\cdot210=44100$

Answer 2

That would be the number of combinations of 6 from 10 multiplied by number combinations of 4 from 10.

10C6 * 10C4

and as 10C6 = 10C4 this

=  (10C4)^2

=  [(10*9*8*7) / (4*3*2*1)^2 

=  210^2 = 44,100 answer