**Quiz
4: Practice Test Chapter 10: Counting Principles MGF 1106 Ambrioso**

**You
should work on the homework as well as the Practice Test at the end of Chapter 10.**

1.
Evaluate* P(*5, 3).

2.
Evaluate *C*(7,
3).

3. Evaluate

4. In how many ways can two letters be chosen from the alphabet?

5. Suppose two dice are thrown. In how many ways can you get a sum of ten?

6. Four people are to pose for a group picture. How many different arrangements are possible if they are to stand in a single row?

7. How many counting numbers less than 450 are divisible by 2 or 3?

8. How many subsets of 4 elements does the set { a, b, c, d, e, f } have?

9. How many distinct arrangements of the letters in the word “letter” are possible?

10. How many different sums of money can be made from a penny, a nickel, a dime, a quarter, and a half-dollar, and a dollar bill if exactly four of these are selected?

11. Given a set with 8 elements. How many subsets of less than 3 elements does it have?

12. You are putting a square slide into a slide projector. How many way can you orient the slide? Note that we are counting all orientations. Only one of them is correct.

13. Draw a tree diagram illustrating the possible outcomes if two letters are chosen from the set {a, b, c } with no repetitions allowed?

14.
You wish to make a small lottery (played like
the

15. A motorcycle license plate consists of 3 letter followed by 2 numbers. How many plates are possible?

16. Suppose you have six textbooks and wish to arrange two of them on a shelf. In how many ways can you arrange them?

17. There are seven women on committee. How many subcommittees an be formed if we must have 3 women on the subcommittee?

18. If 2 married couples are to be arranged in a row, with the couples sitting together, how many arrangements are possible?

19.
In how many ways can two spades be drawn** **if
order is taken into consideration?

20. A committee of six students is to be formed by choosing from a group of 5 boys and 7 girls. If the committee must have 3 boys and 3 girls, how many different committees are possible?