Using Counting in Probability (1 Viewer)

[bleh1234]

This is from exercise 10H, in the Cambridge textbook.
From a standard pack of 52 cards, three are selected at random. Find the probability that: they are from the same suit
the answer is 22/425.
I understand how to do it the 2 unit way (52/52 * 12/51 * 11/50) but i don't know how to work it out using combinations I'm doing (52C1 * 12C2) / 52C3 but im getting 66/425.
Please help!

 

[braintic]

The calculation is 4 times 13C3 / 52C3

ie. pick the suit, then pick 3 cards from 13 in that suit

The reason your answer is wrong is that you are triple counting.
You will choose each hand 3 times.

eg. if the hand is 2H, 3H, 4H ... you will get that hand by first picking 2H then the other two cards .... you will get it again by first picking 3H and then the other two cards .... and yet again by first picking 5H and then the other two cards.

In other words ... you are partially ordering your selection. You are treating 2H..3H..4H and 3H..2H..4H as different hands.

 

[bleh1234]

Thanks!