# Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw two red aces and two black jacks?

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• Anonymous
5 years ago

Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw two red aces and two black jacks?

There are 4 aces in a whole deck...so there are 2 red aces...

There are 4 jacks in a whole deck...so there are 2 black jacks...

You want to choose two red aces out of two, so essentially you are choosing all aces...so 2C2 = 1 way...

AND...

You want to choose two black jacks out of the two in the deck, so you are essentially choosing all the black jacks...so 2C2 = 1 way..

AND...

Remember, this is only 4 cards that are drawn out of 5.

The fifth card is not a black jack or red ace, so there are 52 - 4 = 48 cards that aren't black jacks or red aces, so you want to choose the fifth card out of those 48 cards....(in other terms pick 1 out of 48 cards that aren't red aces or black jacks)...and thus 48C1 = 48 ways...

Now multiply....

2C2 * 2C2 * 48C1

= 1 * 1 * 48

= 48 ways...

There are 48 ways to draw two red aces and two black jacks...