00:01
Alright, so for this problem we're considering a 52 card deck.
00:06
For part a, we're picking out a four card hand.
00:10
We want to know how many different options there are.
00:14
So for our four card hand, the first card, there's 52 cards to choose from.
00:18
Then there's 51, then there's 50, and then there's 49.
00:24
So we multiply those all together.
00:26
We're going to get the total amount of cards and the total amount of hands, which is 6 ,497 ,400.
00:38
So 6 ,497 ,400.
00:42
Now if we're looking at cards with no queens, we know that in a standard deck there are four queen cards.
00:53
So if we want no queens, we would do 52 minus 4, which is 48.
00:58
So our first option, we have 48, then 47, then 46, and then 45.
01:07
Multiply those all together, and we will get that there's a total of 4 ,669 ,920.
01:25
Now for c, we want four cards, one ace.
01:28
So the first one has to be an ace.
01:30
We know that there's four aces, one king of a different color.
01:35
So we know that there's four kings, but we want it to be of a different color.
01:38
So there's three options.
01:40
And then the rest of the cards can be anything.
01:43
So we've chosen two cards, so now we have 50 cards left and 49 cards left.
01:49
So 4 times 3 times 50 times 49, and that's going to give us 294 ,000...