The college of science council has one student representative from each of the five science departments (biology. chemistry, geology. mathematics, physics). in how many ways can3. both a council president and a vice president be selected? b. a president, a vice president, and a secretary be selected? c. two members be selected for the dean's council?

a. 20 b . 60 . c. 10

Step-by-step explanation:

The number of permutation of selecting r things from n things =

The number of permutation of selecting r things from n things =

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 :

∴ 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 :

∴ 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 :

∴ The number of ways a council can select two members for the Dean's Council =10