How many possible 5-card hands from a standard 52-card deck...

How many possible 5-card hands from a standard 52-card deck would consist of the following cards? (a) two spades and three non-spades (b) one face card and four non-face cards (c) three black cards, one heart, and one diamond (a) There are [ ] five-card hands consisting of two spades and three non-spades. (Type a whole number.)

Transcript

00:01 How many five how many possible five card hands from a standard to do tech consist of the falling card? there are two spades and three non spades interesting.

00:11 How many spades are there by the way? spades are a total of 13 of course and the non spades are the rest right other rest which is 39 so the number of ways are going to be out of 13 i choose any two because i need two spades and out of product rule because i need all five and out of 39 i choose any three so that these are the number of it okay they are interested in the whole numbers so we cannot read the answer definitely in terms of c and stuff so i'm just calculating 13 c2 times 39 c3 39 c3 which is coming as 7 1 2 8 4 2 7 1 to 8 4 2 part b 1 face card and 4 non -fifference face card how many face cards are there remember face cards are king queen and jack so there are four decks three face cards each deck so there will be three times four which is 12 12 face cards so definitely the non face cards will be 52 minus 12 which is 40 so the number of ways are going to be out of 12 we choose any one face card out of 40 we choose the rest for non face cards once again calculator 40 40 c4 times 12c1 which is coming as again a big number there's 1 096680 and finally we have three black card one heart and one diamond interesting so how many black cards are there by the way the black cards remember black means spades and clubs so there are 26 black cards and how many heart are there how many heart are there heart will be four and how many diamonds are there diamonds are definitely 13 now there can be a conflict there can be a conflict of of the heart as well because why i'm saying that is it is quite likely that because the three black cards the black cards are three heart is one and the diamond is also one so getting the diamond is not a problem because it's not conflicting with anyone.

02:39 Actually, since there are 26 black cards out of which there are already two hearts and the diamond will also have one heart.

02:48 Right.

02:49 So, uh, okay...

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