a certain box has 8 cards and each card has one of the integers from 1 to 8 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 8 cards ?
"the average of the numbers is 4.5 the total number of ways to choose 2 cards from 8 cards is 8 c 2 = 28 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } the probability is 2 / 28 = 1 / 14 the answer is c ."
divide(const_4, divide(factorial(8), multiply(factorial(2), factorial(subtract(8, 2)))))