A deck of cards contains 5 black cards numbered 5 to 9 and 5 red cards numbered 1 to 5. How many 6-card hands having 4 black cards and 2 red cards can be dealt?

15
50
25
300

Question

A deck of cards contains 5 black cards numbered 5 to 9 and 5 red cards numbered 1 to 5. How many 6-card hands having 4 black cards and 2 red cards can be dealt?

	15
	50
	25
	300

bibby · Answer

You have 10 total cards, and you're getting a 6 card hand. Since you're trying to do 4 blacks and 2 reds, that's 75% black, 5^2 is 25

anonymous · Answer

Thank you for your help guys!

perl · Answer

the numerator is the number of ways (woops i did the probability of dealing that hand)

anonymous · Answer

Thats okay, thank you! Just double checking are the numbers inside the parenthesis being divided?

perl · Answer

the number of ways is 
5 choose 4 * 5 choose 2 = 5 * 10 = 50

perl · Answer

$$ \Large \rm {

 {5 \choose 4 }\cdot {5 \choose 2 }

}$$

perl · Answer

that is a special notation

anonymous · Answer

Ohhh okay gotcha, Thank you!

perl · Answer

also im assuming the order does not count how you deal the cards. what matters is that you have 4 black and 2 red

anonymous · Answer

That sounds about right. Thanks!