Question

In how many ways can 13 cards be selected to obtain 5 spades, 3hearts, 3 clubs, and 2 diamonds?

Answer 1

the number of ways to choose 13 cards out of 52 isi \(\binom{52}{13}\) this is your denominator

the number of ways to choose 5 spades out of 13 is \(\binom{13}{5}\)
the number of ways to choose 3 hearts out of 13 is \(\binom{13}{3}\)
the number of ways to choose 3 clubs out of 13 is \(\binom{13}{3}\) and
the number of ways to choose 2 diamonds is \(\binom{13}{2}\)
multiply those together to get the numerator

Answer 2

oh but wouldn't that give you probability?

Answer 3

@satellite73 that would give you probability. I'm trying to find the number of ways. How would you do that?

Answer 4

yes that gives you the probability
the number of ways you can get the thing you want, divided by the total number of way to get any 13 cards out of 52

Answer 5

before computing it is
\[\frac{\binom{13}{5}\times \binom{13}{3}\times \binom{13}{3}\times \binom{13}{2}}{\binom{52}{13}}\]

Answer 6

i would use a calculator, or better yet wolfram

Answer 7

... that would give you the probability not the number of ways, but i think i get it
another question if the question is like
If a quiz consists of 6 true/false questions. At least 4 must be correct to pass. find the prob that
a) passing b) failing
so i got the prob for passing its 0.0667 so can i use 1-0.0067 for failing or do i have to calculate it like
6/ 6C3 x 6C2 x 6C1 wait would you divide it by 6? so like for a would it be 6/ 6C4 x 6C5 6C6???
@satellite73

Answer 8

if you have the probabibility of passing correct, then your method of finding the probability of failing is correct, but i am not sure the first one is right

Answer 9

the probability of passing is the probability you get 4 right, or 5 right or 6 right

Answer 10

yes