num. of ways to get all-red five-card hand from 52-card deck

Help find the number of ways to get all red cards in a five-card hand from a 52-card deck.

Re: Word Problem

dcc3038026 said:

Help find the number of ways to get all red cards in a five-card hand from a 52-card deck.

Click to expand...

I may be oversimplifying this.....BUT....

How many red cards are there in a deck of 52 cards?

You want to pick 5 of these red cards...and the order does not matter.

Looks like a "combination" problem to me.

Re: Word Problem

The difference between combinations and permutations is rather order matters or not.

In a permutation order matters. In a combination order does not matter.

For instance, a common misnomer is a 'combination' lock. When you want to open a combination lock you have to enter the

numbers in the correct order. It should be called a 'permutation' lock.

Suppose the numbers to open a combination lock were 2 12 34 5 9

If it were truly a combination lock, then you could enter them in any order and it would open.

But a permutation is when order matters, so we have to enter them in that order.

See now a little better?.

Re: Word Problem

I got it, I think.... Please review for feedback......

Total number of cards 52 in one deck
There are total 26 red cards in a 52 card deck

Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards ways of having all are red cards = 26C5

26C5 = 26!/(5!(26-5)!)

= (26x25x24x23x22x21!)/(5!(21)!)
= (26x5x2x23x11)

= 65780 ways >>answer