if 4 people are selected from a group of 6 married couples , what is the probability that none of them would be married to each other ?
"each couple can send only one ` ` representative ' ' to the committee . we can choose 4 couples ( as there should be 4 members ) to send only one ` ` representatives ' ' to the committee in c 46 c 64 # of ways . but these 4 chosen couples can send two persons ( either husband or wife ) : 2 ∗ 2 ∗ 2 ∗ 2 = 242 ∗ 2 ∗ 2 ∗ 2 = 24 . so # of ways to choose 4 people out 6 married couples so that none of them would be married to each other is : c 46 ∗ 24 c 64 ∗ 24 . total # of ways to choose 4 people out of 12 is c 412 c 124 . p = c 46 ∗ 24 c 412 = 1633 p = c 64 ∗ 24 c 124 = 1633 answer : d ."
multiply(multiply(multiply(divide(multiply(6, const_2), multiply(6, const_2)), divide(multiply(4, 4), subtract(multiply(6, const_2), const_1))), divide(subtract(multiply(4, 4), const_2), multiply(4, 4))), divide(subtract(subtract(multiply(4, 4), const_2), const_2), subtract(multiply(4, 4), const_1)))