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
