We want to form a committee by selecting 5 males and 4 females from a group with 15 males and 10 females. How many choices are there?

Question

We want to form a committee by selecting 5 males and 4 females from a group with 15 males and 10 females. How many choices are there?

Answer 1

how many ways can you choose 5 males from a group of 15 males ?

15!/(5!)(15-5)!

15!/(5!)(10!)

(15*14*13*12*11)/(5*4*3*2)

simplifying...

3*7*13*11=3003 ways (15/5=3, 12/4*3=1, 14/2=7)

how many ways can you choose 4 females from a group of 10 females ?

10!/(4!)(10-4)!

10!/(4!)(6!)

(10*9*8*7*)/(4*3*2)

simplifying...

10*3*7=210 ways (9/3=3, 8/4*2=1)

each group of 5 males can be paired with each group of 4 females

there are 3003 groups of males and 210 groups of females

3003*210=630,630 choices of 5 males and 4 females