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:
<u>C </u> <u> AC </u> <u> TD </u>
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 = <u> 20! </u> = <u>20.19.18.17.16!</u> = <u>20.19.18.17</u> = 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 = <u> 15! </u> = <u>15.14.13!</u> = <u>15.14</u> = 105
13! 2! 13! 2.1 2
C₅,₂ = <u> 5! </u> = <u>5.4.3!</u> = <u>5.4</u> = 10
3! 2! 3! 2.1 2