Question

6 people in a house are charged with completing one of three different chores: two people sweep, two people clean bathrooms, and two people do the dishes. How many ways are there of assigning people to do these tasks?

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Number of ways to select 2 people from 6 for sweeping = 6C2 = 15

Number of ways to select 2 people from remaining 4 for cleaning bathrooms = 4C2 = 6

Number of ways to select 2 people from remaining 2 for doing the dishes = 2C2 = 1

Number of ways to assign people to do these tasks = 15 x 6 x 1 = 90