Answer: a. 20 b . 60 . c. 10
Step-by-step explanation:
The number of permutation of selecting r things from n things = [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
The number of permutation of selecting r things from n things = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Given : Number of science departments : n= 5
a . If both a council president and a vice president be selected , so we need to select for 2 positions (order matters).
Number of ways : [tex]^5P_2=\dfrac{5!}{(5-2)!}[/tex]
[tex]=\dfrac{5\times4\times3!}{3!}=20[/tex]
∴ The number of ways a council can select a president and a vice president=20 .
b. If a resident, a vice president, and a secretary be selected, then we need to select for 3 positions (order matters).
Number of ways : [tex]^5P_3=\dfrac{5!}{(5-3)!}[/tex]
[tex]=\dfrac{5\times4\times3\times2!}{2!}=60[/tex]
∴ The number of ways a council can select a resident, a vice president, and a secretary =60.
c. If two members be selected for the Dean's Council , then order not mattes.
Number of ways : [tex]^5C_2=\dfrac{5!}{2!(5-2)!}[/tex]
[tex]=\dfrac{5\times4\times3!}{2\times3!}=10[/tex]
∴ The number of ways a council can select two members for the Dean's Council =10
