MGMAT Q25

[Cybermusings]

Please provide the answer with detailed explanation and alternative solutions

[jayhawk2001]

Hmm, this one had me going for a while.

Total number of possibilities = 12 * 11 * 10 * 9

Out of this, no-pair = 12 * 10 * 8 * 6

So, prob of no-pair = 12*10*8*6 / 12*11*10*9 = 16/33

So, prob of atleast 1 pair = 1 - 16/33 = 17/33


...Alternatively...

Now, I can't seem to solve this the straight way.

Num possibilities for 2 pair = 12 * 6 * 10 * 5
Num possibilities for 1 pair (only) = 12 * 6 * 10 * 8

Summing the above, I get 12*6*10*13 / 12*11*10*9 = 26/33

I'm definitely missing something.