1.Issam has 11 different CDs of which 6 are pop music , 3 are jazz and 2 are classical. Issam makes a selection of 2 pop music CDs, 2 jazz CDs and 1 classical CD. How many different selections can be made.Here the answer is 90 finalized by multiplying all.

2.A committee of 5 people is to be chosen from 6 men and 4 women. In how many ways can this be done If there must be more men than women on the committee.Here we need to add all outcomes.
WHY THESE QUESTIONS NEED ADDITION AND MULTIPLICATION?

There are 6C2 ways to pick the pop CDs, 3C2 ways to pick jazz,and 2C1 ways to pick classical. You multiply because the separate classifications are independent. For each way to pick the jazz, there are 3C2 ways to pick the pop, etc.

For the committee, there are several ways to pick people.
5 men 0 women
4 men 1 woman
3 men 2 women
So figure the combinations for each make-up, and add them together. You need to add, because the various populations are mutually exclusive.

Can you make me clear how various population are mutually exclusive?

come on. You cannot simultaneously have 5 men and only 4 men.

Think about it.

In the first question, we have different categories (pop, jazz, and classical) from which Issam needs to choose CDs. We need to figure out the number of possible selections he can make.

To determine the number of selections, we multiply the number of choices available for each category. In this case, there are 6 choices for pop music CDs, 3 choices for jazz CDs, and 2 choices for classical CDs. Hence, the total number of selections is 6 * 3 * 2 = 36.

However, the question asks for a specific combination of CDs: 2 pop CDs, 2 jazz CDs, and 1 classical CD. To find the number of ways this combination can be selected, we need to consider the different orders in which these categories can appear.

For example, for the pop CDs, there are 6 choices for the first CD and then 5 choices for the second CD (since we cannot choose the same CD twice). Multiplying these together gives us 6 * 5.

Similarly, for the jazz CDs, there are 3 choices for the first CD and then 2 choices for the second CD. Multiplying these together gives us 3 * 2.

For the classical CD, there are 2 choices.

To find the total number of selections, we multiply all of these possibilities together: 6 * 5 * 3 * 2 * 2 = 180.

Therefore, the correct answer is 180, not 90 as you mentioned.

In the second question, we need to choose a committee of 5 people from a pool of 6 men and 4 women, with the condition that there must be more men than women on the committee.

To determine the number of possible ways to choose the committee, we need to consider different scenarios that satisfy the condition.

1. Choosing 3 men and 2 women: There are 6 ways to choose 3 men from 6 men and 4 ways to choose 2 women from 4 women. Hence, there are 6 * 4 = 24 ways to choose 3 men and 2 women.

2. Choosing 4 men and 1 woman: There are 6 ways to choose 4 men from 6 men and 4 ways to choose 1 woman from 4 women. Hence, there are 6 * 4 = 24 ways to choose 4 men and 1 woman.

Adding these two scenarios together, we get 24 + 24 = 48.

Therefore, the correct answer is 48, which is obtained by adding the different outcomes that satisfy the given condition.

In both of these cases, we use addition and multiplication to determine the number of possible outcomes based on the given conditions. Addition is used when we need to consider multiple scenarios separately, and multiplication is used when we need to determine the number of possibilities by considering the choices available for each category in a specific order.