Unit 4

Question 1

How many phone numbers (not including the area code) are possible if the first 3 digits must be 763-_ _ _ _?

Answer 1

10 000

Question 2

How many license plates can be made by using 3 digits followed by 3 letters?

Answer 2

17 576 000

Question 3

How many odd four-digit numbers can be made using (1, 2, 3, 4, 5, 7) if no digit may be repeated?

Answer 3

240

Question 4

If a building has 6 entrances, in how many ways can a person enter and leave a building if no door can be used twice?

Answer 4

30

Question 5

Using the letters in the word “MELFORT”, how many arrangements are possible if the word must start with a consonant?

Answer 5

3600

Question 6

In how many ways can you line up 6 people in a row for a picture?

Answer 6

720

Question 7

What are the formulas for mutually exclusive and not mutually exclusive events?

Answer 7

See notes

Question 8

Which of the following events are mutually exclusive?

Answer 8

a) draw a 5, draw a queen
b) draw a diamond, draw a 10

Question 9

How many possibilities are there for picking an even number or a 5 out of a hat containing the numbers 1 through 9?

Answer 9

5

Question 10

From the set A= (1, 2, 3, 4, 5, 6, 7, 8, 9) how many possibilities are there that a random number chosen at random is either even or less than 5?

Answer 10

6

Question 11

Determine the number of possibilities that you will get a sum of 9 or a sum of 10 when you fill two standard dice.

Answer 11

7

Question 12

Determine the number of possibilities that you will get a sum of 10 or roll at least one 5 when you roll two standard dice.

Answer 12

13

Question 13

How many ways can you line up 50 graduates for grand march?

Answer 13

3.0414 • 10^64

Question 14

There are 10 teams in a tournament. In how many ways can these teams place 1st, 2nd, and 3rd?

Answer 14

720

Question 15

Calculate the number of permutations possible with the letters in the word TUESDAY if every letter is included in each arrangement?

Answer 15

5040

Question 16

Tania needs to create a password for a social networking website she registered with. The password can use any digits from 0 to 9 and/or any letters from the alphabet. The password is case-sensitive so she can use both Lower and upper-case letters. Her password must be a minimum of 5 characters long and a maximum of 7 characters and each character can be used only once in the password. How many different passwords are possible?

Answer 16

2.5237 • 10^12

Question 17

At a used car lot, seven different car models are to be parked close to the street for easy viewing. Three of the seven cars are red and the other four cars are black.
a) The three red cars must be parked so there is a red car at each end, and the third red car is exactly in the middle. How many ways can the seven cars be parked.
b) The three red cars must be parked side by side. How many ways can the seven cars be parked.

Answer 17

a) 144
b) 720

Question 18

Determine the number of permutations possible of the letters in the word HOCUS-POCUS.

Answer 18

226 800

Question 19

Determine the number of permutations of the letters in the word BUBBLE if:
a) there are no restrictions
b) if all arrangements must start with the letter L
c) if all arrangements must start with the letter B

Answer 19

a) 120
B) 20
c) 60

Question 20

If Julie’s home is 3 blocks North and 5 blocks West from her school, how many routes can Julie take from her home to school if she always travels either east or south?

Answer 20

56

Question 21

A library has 10 books on hockey. You are allowed to borrow 4 books at a time. In how many ways can you make your selections?

Answer 21

210

Question 22

A class has 14 students with glasses and 11 students without glasses. You want to choose 4 classroom representatives. In how many ways can the representatives be chosen?

Answer 22

12 650

Question 23

A class has 9 boys and 13 girls. You want to choose 5 classroom representatives. In how many ways can this be done if:
a) there are no further restrictions
b) All 5 representatives are boys
c) all 5 representatives are girls
d) the representatives are a mixture of boys and girls

Answer 23

a) 26 334
b) 126
c) 1287
d) 24 921

Question 24

A school has 10 students on the debate team (7 girls and 3 boys). You need to select 2 boys and 3 girls to represent your school at regionals. In how many ways can you make your selections?

Answer 24

105

Question 25

A soccer team with 12 players has booked 3 hotel rooms for the players. One room has 5 beds, another room has 4 beds, and the third room has 3 beds. Assuming each player will have their own bed, in how many ways can the players be assigned to the rooms?

Answer 25

27 720

Question 26

Monique, Jaqueline and Krista each have a locker on a different floor in the school. They have 15 sweatshirts that they are going to store in their lockers. Monique’s locker has room for 5 sweaters, Jacqueline’s locker has room for 7 sweaters and Krista’s locker has room for 3 sweaters. In how many ways could the sweaters be assigned to the lockers?

Answer 26

360 360

Question 27

How many 6 letter “words” can be made using 2 different vowels and 4 different consonants? (Y is a consonant)

Answer 27

43 092 000

Question 28

A teacher and his students are having a class picture taken. There are 5 boys and 3 girls in the class. The teacher wants the boys to sit together, and the girls to sit together. In how many ways can the teacher and students sit in a row for a picture?

Answer 28

4320

Question 29

Suppose there are 10 different dats items represented by (a, b, c, d, e, f, g, h, i, j) to be placed into 4 memory cells in a computer. Only 3 data items are to be placed in the first cell, 4 data items in the second cell, 2 data items in the third cell and 1 data item in the last cell. How many ways can the 10 data items be placed in the four memory cells?

Answer 29

12 600

Question 30

How many different 5 card hands, that contain at most one black card, can be dealt to one person from a standard deck of cards?

Answer 30

454 480

Question 31

Give the three formulas

Answer 31

Notes