# Counting Principles, card 1..50 and one number is twice the other

• Sep 26th 2010, 04:17 PM
DBA
Counting Principles, card 1..50 and one number is twice the other
There are 50 cards numbered from 1 to 50.
Two different cards are chosen at random. What is the probability that one number is twice the other number?

The answer is 2*25 / 50*49

I tried to split it in two cases. Case1, I get the lower card first (2,4) and case2, I get the higher number first (4,2).

case1:

__ __ First place has 25 choices (1-25), second place then has only 1 choice

case2:

__ __ First place has 25 choices (26-50), second place then has only 1 choice

Then I would add it up: 1*25 + 1*25

The total amount of ways to combine two cards would be 50*49 (First place has 50 choices and second place has 50-1 card which was already used)

The probability is then 1*25 + 1*25 / 50*49

Is this approach correct. The answer indicates that I have to multipy (2*25).

Thanks.
• Sep 27th 2010, 12:09 AM
emakarov
Quote:

The answer is 2*25 / 50*49
It seems that you came up with the same answer: (1*25 + 1*25) / 50*49.

Quote:

Is this approach correct. The answer indicates that I have to multipy (2*25).
I am not sure I understood what you said. Multiply by (2*25)?