Question

Problem check: How many 6 card hands containing no queens and no spades can be chosen from a bridge deck of 52 card?

My attempt: I used the combination formula, but before that, I did 52-8 (4 because of the queens, another 4 for the spades). So I was left with 44!/(38!6!). My result from that...I dunno, I don't feel it is right or if what I was even so.

Answer 1

@shamil98 Raito is a genius, no? :D

Answer 2

Does the 6 not come in to play at all? May I ask how you figured?

Answer 3

Oh sorry, I meant it should be \(\displaystyle\binom{52-8}{6}\). You're choosing only 6 of the total possible cards, which are the original 52, excluding the 4 aces and 4 queens.

Answer 4

Right, and that notation indicates 44!/6!?

Answer 5

Yes

Answer 6

God damn it I was right after I did it again. Thank you so much.

Answer 7

You're welcome!

Answer 8

@SithsAndGiggles 3692043853872845511171702515298077625443942400000000 that does not make sense to me o.o did I do it wrong? Sorry once again o.o

Answer 9

For anyone looking, help is appreciated.

Answer 10

There are 4 queens (including the queen of spades) and 12 spade cards (excluding the queen of spades). Therefore the number of cards to choose from is 52 - 16 = 36. The possible number of combinations is
\[36C6=\frac{36!}{6!30!}=\frac{36\times35\times34\times33\times32\times31}{6\times5\times4\times3\times2\times1}\]

Answer 11

I can't believe I didn't see that...thank you so much.

Answer 12

You're welcome :)

Answer 13

I can't either. Thought it said aces, not spades... sorry!