Counting Techniques Question: Drawing 5 specific cards out of a deck

[student74]

Homework Statement

We draw 5 cards out of a normal deck of 52 cards. No replacements.
How many combinations have exactly one Jack, one Queen, one King?

Homework Equations

The Attempt at a Solution

The solution = 49,920

My attempts:

I keep getting 99,840.

So 4C1 Jack, 4C1 Queen, 4C1 King, then for remaining two cards 40 possible, then 39 possible.

I go 4C1 x 4C1 x 4C1 x 40 x 39 = 99,840

Are there combinations that are repeated somewhere then? :S

 

[Ray Vickson]

Homework Statement

We draw 5 cards out of a normal deck of 52 cards. No replacements.
How many combinations have exactly one Jack, one Queen, one King?

Homework Equations

The Attempt at a Solution

The solution = 49,920

My attempts:

I keep getting 99,840.

So 4C1 Jack, 4C1 Queen, 4C1 King, then for remaining two cards 40 possible, then 39 possible.

I go 4C1 x 4C1 x 4C1 x 40 x 39 = 99,840

Are there combinations that are repeated somewhere then? :S

After choosing 1 Jack, 1 Queen and 1 King you need to choose two more cards from 40. The number of ways of doing that =?

RGV

 

[student74]

oh! thanks Ray! Why doesn't it work going 40 x 39 instead of 40C2? Does 40 x 39 not work because that takes into account order as being relevant?