TEST I. Answer the ff using the ff steps (the keyword, type of problem, given, formula and solving)

1. Assuming the animals are all distinguishable, in how many ways can 4 zebras, 5 lions, and 2 hippos be arranged in a row if :

a. there are no restriction

b. animals of the same kind must be together

c. the hippos are not together

2. In how many ways can search team of 5 members be formed from a group consisting of 3 chemists and 7 physicists if :

a. there is no restriction in the selection

b. the themes include exactly 2 chemists

c. the team must include most 3 physicists

3. A math class consists of 15 boys and 10 girls. In how many ways can committee of 8 members be formed if :

a. the number of boys is more than twice the number of girls

b. mary and ann cannot be in the committee simultaneously

4. In how many ways can five couples be seated in a row if :

a. there are no restriction

b. each couple must be seated together

c. each husband must be seated to the left of his wife

5. A comedian is planning to make his show more appealing by telling 3 jokes at the beginning of each show. He has been black in a bar for the next three months. If he gives one performance and night and he never wants to repeat the same set of jokes on any two nights, what is the minimum number of jokes he needs to prepare?

6. In how many ways can 3 people be selected from 5 japanese, 5 koreans and 5 chinese if each nationality must be represented?