abhicoolmax wrote:
I 100% DON'T agree with GMAT Pill Instructor initial assumption!! No where in the question it says you can assume married couple don't split up.
*Here is the solution in simple terms:*
1. All 4 single = 4C4 = 1
2. 1 married couple included = 3C1* (for the rest 2 there are 3 cases: 2 are single + 1 is married*1 is single + 2 are married)
= 3C1* ( 4C2 + (2C1*2)*4C1 + (2C2*2*2) )
= 3 * (6 + 16 + 4) = 3 * 26 = 78
3. 1 married & 3 single = (3C1*2)*4C3 = 24
4. 2 married & 2 single = (3C2*2*2)*4C2 = 12*6=72
5. 3 married & 1 single = (3C3*2*2*2)*4C1 = 8*4=32
Total = 1+ 78 + 24 + 72 + 32 = 207
I might have done some calculation mistake (forgive me for that), but hope you got the point.
*Alternative approach:* (I always thing of negative approach as if you go to harder levels, GMAT I think likes to test this way of your thinking)
At-most 1 married couple
= Total possible ways - 2 married couple
= 10C4 - 3C2
= 210 - 3
= 207
Hope this helps!
In the first approach I have some doubts
I understood the logic and cases but in the case of 1 married couple included I am doing: 3c1*2c2* 4c2
3c1=no of ways to choose 1 couple out of 3
4c2=no of ways to choose 2 single out of 4
2c2=choosing both persons from the couple selected
Can you explain where I am wrong?