Combinations 2?

Question

Ugh...I am stuck on this other question too...

The game of euchre uses only the 9s, 10s, jacks, queens, kings and aces from a standard deck of cards. How many five-card hands have...

a) all red cards?
b) at least two red cards?
c) at most two red cards

I dont know how to go about with these questions, and keep on getting the wrong answers...

Please help me

Thanks

Answer 1

a) choose 5 red cards out of the 12.
that's 12 choose 5 = 792

b) break it up into possibilities
(12 choose 2) (12 choose 3) = 14520
(12 choose 3) (12 choose 2) = 14520
(12 choose 4) (12 choose 1) = 5940
(12 choose 5) (12 choose 0) = 792

Where those represent hands with exactly 2, 3, 4, or 5 red cards. Sum: 35772

c) like before, only we do hands with exactly 0, 1, or 2 red cards:
(12 choose 2) (12 choose 3) = 14520
(12 choose 1) (12 choose 4) = 5940
(12 choose 0) (12 choose 5) = 792
Sum: 21252

Answer 2

The euchre deck has 24 cards, half red and half black.

For all red cards, you have to pick 5 out of the 12.  This number is 12!/(7!*5!) or 792.

To get the number with at least two red cards, calculate the number of hands with 2, 3 and 4 red cards and add to 792.

For at most two red cards, calculate the number with 0 and 1 red cards and add to 792.

Answer 3

a) all red
12C5 = 792 hands
b) at least 2 red
0 red 792
1 red = 12*(12C4) = 5,940
2 red = (12/1)(11/2)(12/1)(11/2)(10/3) = 14,520
3 red = 14,520
4 red = 5,940
5 red = 792
42,504 total hands

b) at least 2 red
42,504 - 5,940 - 792 = 35,772 hands

c) at most 2 red
14,520 + 5,940 + 792 = 21252 hands

Answer 4

a. 12C5/24C5
b. (12C2+ 12C3+12C4+12C5)/24C5
c. (12C3+12C4+12C5)/24C5


im not sure of of the answers if they r incorrect plz tell me the correct answers ]\

thankyou

Answer 5

a) all red cards
C(12,5)
b) at least two red cards
[C(12,2)C(12,3)+C(12,3)C(12,2)
+C(12,4)C(12,1)
+C(12,5)C(12,0)]
c) at most two red cards
[C(12,0)C(12,5)+C(12,1)C(12,4)
+C(12,2)C(12,3)]