probability drawing cards?

There are 52 C 5 ways to draw 5 cards = 2598960

Of these, 13 x 48 are of the desired kind

(13 different ranks that can match, 48 other cards),

624 / 2598960 or 1 / 4165 or .00024 or 0.024 %

Another approach:

Chances of first 4 matching and fifth not are:

1 x 3/51 x 2/50 x 1/49 x 1

= 6/124950

but odd card can occur anywhere along the way,

so we multiply by 5

30/124950 = 1 / 4165 = .00024

( Actual number is 0.00240096038 )

.

Well, the first time you have a 4/52 chance, the second draw you have a 3/51 chance, the third time you have a 2/50 chance, and the final draw you have a 1/49 chance.

Then just multiply the fractions together and you get a 1/270725

5C3 is a shorthand way of writing 5!/3!(5 -3)! = [5*4*3*2*1]/[(1*2*3)*(1*2)] = 10