Respuesta :
Answer:
(a) There are 20 ways to select both a council president and a vice president.
(b) There are 60 ways to select both a president, a vice president, and a secretary.
(c) There are 10 ways to select two members for the President’s Council.
Step-by-step explanation:
All the five engineering majors have one student representative at the Student Engineers Council at a California university.
(a)
Compute the number of ways to select both a council president and a vice president as follows:
As order of selection is important, the number of ways to select both a council president and a vice president is:
[tex]^{5}P_{2}=\frac{5!}{(5-2)!}=20[/tex]
Thus, there are 20 ways to select both a council president and a vice president.
(b)
Compute the number of ways to select president, a vice president, and a secretary as follows:
Again as the order of selection is important, the number of ways to select both a president, a vice president, and a secretary is:
[tex]^{5}P_{3}=\frac{5!}{(5-3)!}=60[/tex]
Thus, there are 60 ways to select both a president, a vice president, and a secretary.
(c)
Now for two members for the President's Council are to be selected.
As the order of selection is not important, two members can be selected in:
[tex]{5\choose 2}=\frac{5!}{(5-2)!\cdot\ 2!}=\frac{5!}{3!\ \times\ 2!}=10[/tex]
Thus, there are 10 ways to select two members for the President’s Council.
