Confused on Combinatorics Strategy

[TWN]

Below are 2 combinatoric problems. Both use the same strategy except for the last step, why do I use addition on one of these problems and multiplication on the other?

The 1st problem:
A second grade class is writing reports on birds. The students' teacher has given them a list of 6 birds they can choose to write about. If lizzie wants to write a report that includes two or three ofo the birds, how many different reports can she write?

6! = 15
4!2!

6! = 20
3!3!

15 + 20= 35 WHY DO WE USE ADDITION IN THIS CASE AND IN THE BELOW CASE......

The 2nd problem
The I Eta Pi fraternity must choose a delegation of three senior members and two junior members for an annual interfraternity conference. If I Eta Pi has 12 senior members and 11 junior members, how many different delegations are possible?

12! = 220
9!3!

11! = 55
9!2!

220 * 55 = 12,100....HOW COME IN THIS CASE WE MULTIPLY??? All help is appreciated.

[d2rockstar]

Originally Posted by TWN

Below are 2 combinatoric problems. Both use the same strategy except for the last step, why do I use addition on one of these problems and multiplication on the other?

The 1st problem:
A second grade class is writing reports on birds. The students' teacher has given them a list of 6 birds they can choose to write about. If lizzie wants to write a report that includes two or three ofo the birds, how many different reports can she write?

6! = 15
4!2!

6! = 20
3!3!

15 + 20= 35 WHY DO WE USE ADDITION IN THIS CASE AND IN THE BELOW CASE......

The 2nd problem
The I Eta Pi fraternity must choose a delegation of three senior members and two junior members for an annual interfraternity conference. If I Eta Pi has 12 senior members and 11 junior members, how many different delegations are possible?

12! = 220
9!3!

11! = 55
9!2!

220 * 55 = 12,100....HOW COME IN THIS CASE WE MULTIPLY??? All help is appreciated.

Remember this:

If the operation to be performed is x or y than we add. In question 1 either 2 or 3 birds. Hence add both the operations.

If the operation to be performed is x and y than multiply. In the 2nd question select 3 out of 12 senior members and 2 out of 11 junior members.
Here we find number of ways of selecting senior members and number of ways of selecting junior members and we multiply them

Thanks,
Quant-Master

[TWN]

Thanks!