Name: Navi

Who is asking: Student
Level: Secondary

Question:
For this question I can't figure out answer for part "c"

Q: A ski trip at the school has been arranged. there are 30 students that have paid for the trip and 6 parents that have volunteered to chaperone. to transport the students and parents easily, they are to be divided into two group. one group has 10 students and 2 parents, and the other group has 20 students and 4 parents.

(a) How many different group of 10 students can be formed?
ANSWER: 10!= 3628800

(b) How many different groups consistinmg of 10 students and 2 parents are possible?
ANSWER: 10C2= 45

(c) kelly is one of the students going on the ski trip, and kelly's mother volunteered to be one of the chaperones. kelly's mother would prefer to be in the smaller group and not in the same group as kelly. if this wish is honoured, how many ways can the smaller group and its chaperones be chosen?
ANSWER:

For part (a) you have 30 students and you are to choose 10 of them to be in the small group. The number of ways of choosing 10 things from 30 things is 30C10 (that's why it is called "30 choose 10"). Thus the answer to (a) is 30C10.

For part (b) think of it in two steps. First you select 10 students which you can do in 30C10 ways. To each of these groups of 10 students you can now add 2 parents. There are 6 parents to choose from so the number of ways of choosing the 2 parents is 6C2. Thus the number of different groups consisting of 10 students and 2 parents is 30C10 times 6C2.

For (c), to comply with her request you need to construct the small group by choosing 10 students from 29 students (all the students except Kelly) and 1 parent from 5 (all the parents except Kelly's mother).