JAI HIND wrote:

There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group?

I solved this. But wanna check if you guys have a shorter method.

I'm not too good at perm/comb, but here goes:

10 ways to pick the first person, 8 ways to pick the second (b/c the 1st person's spouse must be excluded), and 6 ways to pick the 3rd (b/c the 2nd person's spouse must be excluded).

Therefore,

(10*8*6)/3! since order does not matter.

Answer: 80