check my probability answer...plz..?

Question

using a standard deck of cards how many 5-card hands are possible that have 3 aces and 2 kings??.....i used combinatorics and i got 24.....is it right? if not how do u get the right answer...

Answer 1

there are 4 Aces and 4 kings

choose 3 out of 4:
4C3

choose 2 out of 4
4C2

use principle of counting
4C3 * 4C2

4 x 6

24

yes, you are correct

Answer 2

I "think" I have this right. Probability can be thought of differently:

Think of it this way

Of the 13 different values of cards, you need to choose 1 (let's say aces)

then choose 3 of the 4 aces

then of the remaining 12 values, choose the other one you need (the kings)


out of the 4 kings, choose 2

All those are combinations, not permutations since order doesn't matter. I get an answer over 7,000 just to let you know.

I'll have to check back later to see if I'm right on this one.

Answer 3

There's four ways to determine the ace that isn't in the hand and (4 choose 2)=6 ways to choose the kings that are in the hand so 4*6=24, you are correct.

Answer 4

4C3 * 4C2 = 4*6 = 24