Question

Consider a classroom with 10 students, including 3 of your friends (you are not in the class). Suppose you are waiting outside the room to meet the 3 friends after the class. Assume that people leave the room in fully random fashion. What is the probability that the first three people leaving the room will be your friends? Express your answer as a fraction in its simplest form.

Answer 1

Combination formula: nCr = n!/(r! x (n-r)!)

P(first three people leaving the room will be your friends) = 1/Number of ways in which 3 out of 10 people can come out

= 1/10C3

= 1/[10!/(3! x 7!)]

= 1/120