Question

A lottery ball drawing machine has 50 balls, each labeled with a distinct integer from 1 to 50. Every Sunday, four different balls are drawn to determine the winning numbers. You have last Sunday's ticket with the numbers {3,7,12,15}. You missed the drawing, but heard that 15 was the largest of the four numbers. How many such sequences of 4 integers are there?

Answer 1

since we know 15 is the largest of 4 numbers, we only have to worry about the ways to choose 3 numbers from 14:

C(14,3) = 14*13*12/6 = 364