Statistical Question

[Easy n Dirty]

What are the percentage chances of being able to cash twice with seven cards?

I'm thinking it's 2 out of 3 (same as being able to cash once in four cards), but I am far from certain.

[banana_hammocks]

i would assume it would be slightly better than that as you get to choose which you cash, so can look ahead and best maximise your chances of getting 2 sets.

But it is at least 2/3

[hecter]

It's higher than that... Ultimately, you have these possibilities:
7 blue
7 red
7 green
6 blue 1 red
6 blue 1 green
6 green 1 blue
6 green 1 red
6 red 1 blue
6 red 1 green
5 blue 2 red
5 blue 2 green
5 green 2 blue
5 green 2 red
5 red 2 blue
5 red 2 green
5 blue 1 red 1 green
5 green 1 blue 1 red
5 red 1 blue 1 green
4 red 3 blue
4 red 3 green
4 green 3 blue
4 green 3 red
4 blue 3 red
4 blue 3 green
4 blue 2 red 1 green
4 blue 2 green 1 red
4 red 2 blue 1 green
4 red 2 green 1 blue
4 green 2 blue 1 red
4 green 2 red 1 blue
3 blue 3 red 1 green
3 blue 3 green 1 red
3 red 3 green 1 blue
3 blue 2 red 2 green
3 green 2 blue 2 red
3 red 2 blue 2 green
So, correct me if I'm wrong, but thats 30/36, or 83.3%.

[wcaclimbing]

looks good hecter.

[Splash_x]

It's higher than that... Ultimately, you have these possibilities:
7 blue
7 red
7 green
6 blue 1 red
6 blue 1 green
6 green 1 blue
6 green 1 red
6 red 1 blue
6 red 1 green
5 blue 2 red
5 blue 2 green
5 green 2 blue
5 green 2 red
5 red 2 blue
5 red 2 green
5 blue 1 red 1 green
5 green 1 blue 1 red
5 red 1 blue 1 green
4 red 3 blue
4 red 3 green
4 green 3 blue
4 green 3 red
4 blue 3 red
4 blue 3 green
4 blue 2 red 1 green
4 blue 2 green 1 red
4 red 2 blue 1 green
4 red 2 green 1 blue
4 green 2 blue 1 red
4 green 2 red 1 blue
3 blue 3 red 1 green
3 blue 3 green 1 red
3 red 3 green 1 blue
3 blue 2 red 2 green
3 green 2 blue 2 red
3 red 2 blue 2 green
So, correct me if I'm wrong, but thats 30/36, or 83.3%.

WOW.... so much... math... brain.. exploding