Departments A, B, and C have 10 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?
Select
A) 19,000  B) 40,000  C) 100,000  D) 190,000  E) 400,000
Take the task of creating the task force and break it into stages.   Stage 1: Select one person from department A   There are 10 people to choose from, so we can complete stage 1 in 10 ways   Stage 2: Select one person from department B   There are 10 people to choose from, so we can complete stage 2 in 10 ways   Stage 3: Select one person from department C   There are 10 people to choose from, so we can complete stage 3 in 10 ways   Stage 4: Select 2 people from department D   Since the order in which we select the 2 people does not matter, we can use combinations.   We can select 2 people from 20 people in 20C2 ways (190 ways)   So, we can complete stage 4 in 190 ways   By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a task force) in (10)(10)(10)(190) ways (= 190,000 ways)   Answer:190,000
<result>D</result>
Departments A, B, and C have 10 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?