How many different hands can be dealt in this variant of Poker?

[Firepanda]

In a varient of Poker each player is dealt a hand of 6 cards from a standard pack How many hands are there of each of the following types?

Three pairs: Two cards of the same value. another 2 of a differnt value, and a 3rd paid of a third value. i.e Q(clubs) Q(diamonds) 6(hearts) 6(diamonds) 4(spades) 4(hearts)

..

For my attempt I started with 13C3 + 12C3 +11C3 ... + 3C3 = 1001 different hands

But this hasn't accounted for the differnt variation of suits, threre are 6 possible pairs of suits, so i multiply 1001 by 6?

thanks for any help!

 

[Firepanda]

noone? :(

 

[tiny-tim]

Hi Firepanda!

For my attempt I started with 13C3 + 12C3 +11C3 ... + 3C3 = 1001 different hands

erm … 13C3 is the number of ways of choosing 3 cards out of 13 … but what did you think was the reason for adding 12C3 etc?

Be systematic. One step at a time.

First step: there have to be three different numbers (eg 2 5 Q).

Second step: for each number, there have to be 2 cards of that number.

Try it that way!