Question

How many different ways are there to choose a chairman, assistant chairman, and a treasurer department of 20 people? How many ways are there to choose a committee of 4 people from this same committee? If the committee is required to be comprised of 2 women and 2 men, and there are 5 women in the department, how many different committees are possible?

Answer 1

Answer:

1) 6840

2) 4845

3) 1050

Step-by-step explanation:

1) How many different ways are there to choose a chairman, assistant chairman, and a treasurer department of 20 people?

As it ordered:

C   AC   TD  

20    19      18   = 20.19.18 = 6840

2) How many ways are there to choose a committee of 4 people from this same committee?

Not ordered:

C₂₀,₄ = 20!   = 20.19.18.17.16! = 20.19.18.17 = 4845

         16! 4!        16! 4.3.2.1             4.3.2.1

3) If the committee is required to be comprised of 2 women and 2 men, and there are 5 women in the department, how many different committees are possible?

5 women and 15 men

committee: 2 w and 2 m

C₁₅,₂*C₅,₂ = 105*10=1050

C₁₅,₂ = 15!   = 15.14.13! = 15.14 = 105

         13! 2!     13! 2.1           2

C₅,₂ = 5!   = 5.4.3! = 5.4 = 10

         3! 2!   3! 2.1      2