Ellen draws five cards from a standard deck of 52 cards. In how many ways (a) can her selection result in a hand with no clubs, (b) can the 5-card selections contain at least on club?

Question

Ellen draws five cards from a standard deck of 52 cards.  In how many ways (a) can her selection result in a hand with no clubs, (b) can the 5-card selections contain at least on club?

anonymous · Answer

there are 13 clubs and therefore $39$ not clubs
compute 
$$\frac{\binom{39}{5}}{\binom{52}{5}}$$

anonymous · Answer

What about b)?

anonymous · Answer

at least one means "not none"
find the answer above, subtract it from 1

anonymous · Answer

for a) I get 0.2216, but that doesn't make sense for the question

anonymous · Answer

why not?

anonymous · Answer

did you mean subtract rather than divide?

anonymous · Answer

In how many ways can her selection result in a hand with no clubs?  0.2216, not even 1 :/ i think it's 22%, but i need an actual number

anonymous · Answer

is it 22% of 52! / 5!*48! ?

anonymous · Answer

er sorry 52! / (5! * 47!)

anonymous · Answer

here is the answer to the first one http://www.wolframalpha.com/input/?i=%2839+choose+5%29%2F%2852+choose+5%29

anonymous · Answer

answer to the second one is one minus that number

anonymous · Answer

but the question isn't asking for a percentage, just the amount of times

anonymous · Answer

looks like about 22% or so

anonymous · Answer

there are 2598960 total possibilities, is it 2598960 * .22?