WorksheetsCounting Methods
Total questions: 33
Worksheet time: 2hrs 3mins
Name
Class
Date
1.
You are about to take 6 question test. Each question has 4 possible answer choices. How many ways can you answer the test if you answer each question?
a)
4096
b)
24
c)
1296
d)
10
2.
At a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?
a)
180
b)
23
c)
12
d)
60
3.
Find the number of batting orders for 9 players.
a)
362,880
b)
1
c)
81
d)
72
4.
There are 6 roads from Ponder to Justin, 2 roads from Justin to Halslet, and 3 roads from Haslet to Saginaw. How many possible routes are there from Ponder to Saginaw using only these roads and no backtracking?
a)
12
b)
11
c)
18
d)
36
5.
The Social Security number contains nine digits, if the form of 000-00-0000. How many different Social Security numbers can be formed using any numerals from 0 to 9?
a)
9,000,000,000
b)
81
c)
387,420,489
d)
1,000,000,000
6.
A combination lock has 7 digits. How many distinct combinations does this lock have if the numbers used have to be 0 through 5?
a)
279936
b)
78125
c)
823543
d)
16807
7.
How many ways can the letters in the word PARALLEL be arranged?
a)
40,320
b)
1
c)
3360
d)
64
8.
How many distinct ways can the letters in the word OPPORTUNITIES be arranged?
a)
389,188,800
b)
2,028,377,600
c)
1,556,755,200
d)
16,227,020,800
9.
9 runners are racing. In how many ways can they come in 1st, 2nd and 3rd place?
a)
362,880
b)
9
c)
308
d)
504
10.
Student council has 24 members. In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected? (Order matters)
a)
5,100,480
b)
0
c)
42,504
d)
5.17 x 1021
11.
Jackie wants to select 4 of her 12 books to bring with her on vacation. In how many ways can Jackie make her selection?
a)
48
b)
11880
c)
495
d)
24
12.
Tricia wants to place her 10 DVDs on a shelf. How many arrangements are there for her DVDs?
a)
100
b)
3628800
c)
1
d)
10
13.
One internet site requires you to create a password consisting of 2 letters followed by 4 digits. The digits may not be repeated. How many different passwords can be created?
a)
6760000
b)
3276000
c)
92
d)
3407040
14.
One bank assigns each customer an 8 digit account number. The number 0 can not be used as the first digit. The last digit must be even. How many account numbers can be created?
a)
45000000
b)
100000000
c)
90000000
d)
16777216
15.
In a certain card game, only the number cards (from 2 - 10) are used. Therefore, the entire deck of cards consists of only 36 cards. Each player is dealt 6 cards. How many different 6-card hands are possible, assuming the same 6 cards in different orders are counted as different hands?
a)
216
b)
2176782336
c)
1402410240
d)
1947792
16.
4 children from the same family are all getting their hair cut by the same barber. How many different arrangements are possible for the children to see the barber?
a)
16
b)
256
c)
1
d)
24
17.
How many ways can a club select a president, vice president, and a secretary from a group of 5 people?
a)
12
b)
60
c)
15
18.
What is the value of 5!
a)
25
b)
15
c)
120
d)
720
19.
In how many ways can 3 different Skittles be arranged on a table?
a)
3
b)
9
c)
6
d)
12
20.
How many ways can 8 cheerleaders be chosen for 3 positions on the cheer team?
a)
24
b)
56
c)
128
d)
336
21.
7!
a)
4050
b)
5400
c)
5040
d)
4500
22.
How many different arrangements can be made from the word WATER?
a)
5
b)
120
c)
10
d)
0
23.
How many different arrangements can be made from the word MATH?
a)
10
b)
0
c)
6
d)
24
24.
Simplify the expression 6!/2!
a)
12
b)
360
c)
30
d)
10
25.
What is the value of 8!
a)
40320
b)
36
c)
362880
d)
5040
26.
10! ÷ 9!
a)
900
b)
1
c)
9
d)
10
27.
Find the total number of outcomes for picking a day of the week and a month of the year.
a)
19
b)
84
c)
60
d)
210
28.
A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there?
a)
64
b)
14
c)
24,024
d)
2184
29.
A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals.
a)
135
b)
85,140
c)
14,190
d)
91,125
30.
A lock has four dials. On each dial are the digits 0 to 9. How many possible combinations are there?
a)
40
b)
5040
c)
6561
d)
10,000
31.
The value of 5! is ____.
a)
25
b)
15
c)
120
d)
720
32.
How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits? Think: Does order matter?
a)
90
b)
100
c)
12
d)
24
33.
Ambry must submit 4 paintings as part of her application to art school. If she has 25 to choose from, how many ways can she pick 4? Think: Does order matter?
a)
12,650
b)
303,600
c)
100
d)
254
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