Question

Question 1

1. A telemarketer is given a list of names to contact for a survey on banking services.   He has 40 names per page and must try to complete 5 surveys per hour. How many ways are there to choose 5 names randomly?
2. A parent is making goody bags for their child’s 7^th birthday party. They want to place 2 of 24 chocolate bars, 1 of 12 potato chip bags, 3 of 24 lollipops, and 3 of 20 assorted wrapped candies into each bag. How many different goody bags can be made?

Answer 1

a) There are total of 40 names on each page. We have to choose 5 names randomly.

The number of ways in which this can be done is:

This was done because the choice of the names is independent of the way that the names are chosen and hence the problem is a combinatorial one.

b) For each of the bags, 2 out of 24 chocolate bars, 1 out of 12 potato chip bags, 3 out of 24 lollipops and 3 out of 20 assorted wrapped candies are placed.

Hence, for each of the items, the number of bags that they can be placed are:

Therefore, the number of bags that can be produced in the given way will be the minimum of these numbers which is 6.67. Since, 6.67 bags can't be made, we choose an integer that is smaller and is closest to 6.67. This number is 6.

Hence, a total of 6 goody bags can be made in this way.