Question

Ms. Johnson has to pick a student council of two students. She is given a list of nine students to choose from. How many different councils are possible?

a) 18
b) 36
c) 72
d) 144

Answer 1

To find the number of different student councils possible, we use the concept of combinations. Plugging the values into the formula, there are 36 different councils that Ms. Johnson can choose from.

Step-by-step explanation:

To find the number of different student councils possible, we need to use the concept of combinations. Since Ms. Johnson can pick two students out of nine, we can use the formula for combinations, which is nCr = n! / (r!(n-r)!).

In this case, n (total number of students) is 9 and r (number of students to be chosen) is 2. Plugging these values into the formula, we get:

nCr = 9! / (2!(9-2)!)

nCr = 9! / (2!7!)

nCr = (9 * 8 * 7!) / (2!7!)

nCr = (9 * 8) / 2!

nCr = 72 / 2

nCr = 36

Therefore, there are 36 different councils that Ms. Johnson can choose from.