A box of valentine candy hearts contains 52 hearts of which 19 are white, 10 are tan, 7 are pink, 3 are purple, 5 are yellow, 2 are orange and 6 are green. If you select 9 pieces at random (without replacing any), what is the probability that 3 are white, 2 are tan, 1 is pink, 1 is yellow and 2 are green?
(n/r) = n! / r!(n-r)!
The Attempt at a Solution
So you select 9 pieces at random... you want to draw 3 that are white and there at 19 white total out of 52 possible, so the chance of getting a white on your first draw is 19/52, then 18/51, then 17/50,
for 2 tan out of 10 tan with 50 remaining, i'd go 9/49 then 8/48.
I would continue this process for all colors then multiply these fractions together, is this correct? if not can somebody give me some insight?