preyshi wrote:

9 people, including 3 couples , are to be seated in a row of 9 chairs.

What is the probability that

a. None of the Couples are together

b. Only one couple is together

c. All the couples are together

**Quote:**

a. None of the Couples are together

(1)total # of ways = 9!

(2)One couple is together => 8! *2 - 7!*2*2 - 6!*2*2*2

(3) two couples are together => 7!*2*2 - 6! *2*2*2 ways

(4)three couples are together => 6! *2*2*2 ways

none are together = (1) - (2) - (3) - (4) / (1)

**Quote:**

b. Only one couple is together

(2) One couple is together => 8! *2 - 7!*2*2 - 6!*2*2*2

prob => (2) / 9!

**Quote:**

c. All the couples are together

(4) three couples are together => 6! *2*2*2 ways

prob => (4) /9!