Question

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 ‘words’ can be made from the name ESTABROK

a) with no restrictions?

b) if the ‘word’ must start with an E?

c) if the ‘word’ must start with an S or an E?

d) if the ‘word’ must start with the smaller word ‘BRAT’

7. 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?

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

9. You work as a health inspector and must visit each of the 15 restaurants in town once each week.

a) In how many different orders can you make these inspections?

b) If you were to work 50 weeks a year and use a different order every week, how long would it take you to try all of the different possible orders?

10. Five cards are dealt form 52.

a) How many different hands can be dealt?

b) How many hands will contain 4 hearts?

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 red cards?

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

g) How many will contain at least 2 hearts?

11. Twelve 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?

12. A student is asked to answer seven 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

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

14. In how many ways can a transportation committee of fifteen senators be chosen from the 100 members of the U.S Senate, then a 10 member health committee be formed?

15. Theoretically, how many possibilities are there for first, second, and third place in a marath

Answer 1

1:

Let H shows the head and T shows the tail Following is the tree diagram:

(2)

There are 26 letters and 10 digits.

The possible number of plates with 3 letters and 3 numbers :

In the number plate each letter can be selected in 26 ways and each digit can be selected in 10 ways so possible number of number plates is

The possible number of plates with 4 letters and 3 numbers :

In the number plate each letter can be selected in 26 ways and each digit can be selected in 10 ways so possible number of number plates is

The number of different licence plates is 18,032,976.