solve the best you can

1. Use a tree diagram to show, or list, all possible outcomes when you toss a coin 3 times.

2. Licence plates consist of either 3 letters and 3 numbers or 4 letters and 3 numbers. How many different licence plates can be issued?

3a) In how many ways can a committee of three be selected from 12 students?

b) In how many ways can a president, secretary, and treasurer be chosen from 12 students?

4. How many ways can 11 Redcoat basketball players and Coach Woodburn (12 people) be arranged along the sidelines:

a) with no restrictions.

b) if Coach Woodburn must be at one end of the bench?

c) if Travis and Pat must stand together?

d) if Travis, Pat, and Woody must stand together?

e) if Travis and Pat must be kept separated?

5. In how many ways can a committee of three men and two women from eight men and six women?

6. How many 4 digit numbers can be formed using only the numbers 3 2 7 6 0 4 9 if:

a) there are no repeats allowed?

b) the number is odd and no repeats allowed?

c) the number is greater than 4000 and no repeats are allowed?

d) the number is greater than 4000 and repeats are allowed?

7. In how many ways can a committee of five be selected from nine men and eight women if Miss Jones refuses to serve on the same committee as Mr. Smith?

8. Five cards are dealt form 52.

a) How many different hands can be dealt?

b) How many hands will contain 4 diamonds?

c) How many hands will contain no face cards?

d) How many hands will contain only spades or only clubs?

e) How many hands will contain only black cards?

f) How many will contain no more than 2 face cards?

g) How many will contain at least 2 clubs?

9. Thirteen girls try out for the hockey team. Two play goal, four play defence, and the rest play forward. How many different starting lineups could the coach choose if she needs 1 goalie, 2 defence, and 3 forwards?

10. A student is asked to answer eight of ten questions on a test. How many different ways can a selection of questions occur if:

a) there are no restrictions

b) if there are five questions that must be answered

11. A sportswriter makes his pre-season picks for the top ten teams finish. If there are thirty teams, how many different lists could there be?

12. Theoretically, how many possibilities are there for first, second, and third place in a marathon with 55 entries?

12. Theoretically, how many possibilities are there for first, second, and third place in a marathon with 55 entries?