Question

In my grade 10 class there are there are 16 boys and 9 girls. I need to send 10 of them to a Guidance meeting. How many ways can...

a) an equal number of each gender be chosen?

b) Christopher be chosen?

c) Christopher and Emma be chosen?

d) at least one girl be chosen?

e) Christopher and Emma cannot both go, at least 1 of them must stay in class!

f) Send only girls?

Clearly label each part and show your calculations.

Answer 1

(a)

To choose equal number of each gender we have to select 5 boys and 5 girls.

Number of ways to do so is given by

(b)

Christopher is to be chosen.

So, we have choose 10-1 = 9 students from remaining 16+9-1 = 24 students.

Number of ways to do so is given by

(c)

Christopher and Emma are to be chosen.

So, we have choose 10-2 = 8 students from remaining 16+9-2 = 23 students.

Number of ways to do so is given by

(d)

This can be calculated by subtracting number of ways to choose without any girl from all number of choices.

Number of ways to do so is given by

(e)

We have to exclude those choices where both of Christopher and Emma were selected.

Number of ways to do so is given by

(f)

We have to send only girls. There are 9 girls only. But we have to send 10 students.

Hence, sending only girls is not possible.