A teacher has 10 boys and 12 girls in her grade school class. In how many ways can she select 9 of the children to be in a play if she must select 4 boys and 5 girls.

Question

kinggeorge · Answer

Do you have a guess as to what the answer is?

anonymous · Answer

A)	13,860
	B)	41,580
	C)	55,440
	D)	95,040
	E)	103,950
	F)	124,740
	G)	166,320
	H)	194,040
	I)	none of these

callisto · Answer

I think the calculation is like this
10C4 x 12C5
10C4 -> you need to select 4 boys from 10 boys in which order of selection is not important
12C5 ->you need to select 5 girls from 12 girls in which order of selection is not important
It is an 'and' case, so multiply them
Not sure if it is correct :(

kinggeorge · Answer

Your method is correct.

callisto · Answer

By the way, you'd better write 
P(4boys and 5 girls) =10C4 x 12C5 = ...

kinggeorge · Answer

@Lili24 now that you have the method, can you finish the calculations?

anonymous · Answer

Nope! Im confused :(

callisto · Answer

Have you learnt combination and permutation?

kinggeorge · Answer

10C4 x 12C5=$${10! \over 4!(10-4)!} \times {12! \over 5!(12-5)!}$$With a calculator, this should be easy (if your calculator has the factorial function)

anonymous · Answer

That makes it clear. Thank you both ;)

anonymous · Answer

Is the answer 166,320?

kinggeorge · Answer

Had to leave for a bit, but 166,320 is correct.