Question

at a certain high school, the prom committee is going to choose new members. there are 8 students from the junior class and 5 students from the senior class who are willing to be new members. in how many ways can 7 new members be chosen if fewer than 3 must be from the senior class?

Answer 1

Given there are 8 students from the junior class and 5 students from the senior class who are willing to be new members.

7 new members will be chosen if fewer than 3 must be from the senior class.

If we choose 1 from the senior class, we will choose 6 from the junior class

So, the number of ways = 8C6 * 5C1

If we choose 2 from the senior class, we will choose 5 from the junior class

So, the number of ways = 8C5 * 5C2

So, the total number of ways =

`(8C6\cdot5C1)+(8C5\cdot5C2)=700`

So, the answer will be the total number of ways = 700