1. The digits 5, 6, 7, and 4 are to be arranged to form a 7-digit integer. How many different integers can be formed? A. 5,674 В. 16,384 С. 840 D. 24

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Question
Let's Evaluate
Directions: Choose the letter of the correct answer. Write the chosen letter on a separate sheet
of paper.
1. The digits 5, 6, 7, and 4 are to be arranged to form a 7-digit integer. How many different
integers can be formed?
A. 5,674
В. 16,384
C. 840
D. 24
2. In how many ways can the letters of the word REFERENCE be arranged?
A. 362,880
B. 181,440
С. 7,560
D. 15,120
3. In how many ways can the letters of the word MATHEMATICS be arranged?
B. 39,916.800
A. 6,652,800
C. 4,989,600
D. 55,400
4. A mathematician, a physicist, and an engineer walk into a bar. If there are 3 seats
available at the bar, how many ways are there for the mathematician, physicist, and
engineer to seat themselves?
A. 6
В. 4
С. 1
D. 0
11
5. The mathematician, physicist, engineer, and computer scientist decided to move from
the bar to a (circular) table. They file to the table, staying in order as they sit down, and
wind up seated as shown below.
Engineer
Computer
Scientist
Physicist
Mathematician
How many different seating arrangements at the bar will lead to the seating
arrangement around the table in the image above?
A. 0
В. 1
С. 4
D. 6
6. Six friends Andy, Bandy, Candy, Dandy, Endy and Fandy want to form a club. They
decide that there will be 1 president, 1 secretary and 4 ordinary members. How many
ways can they organize this club?
A. 720
В. 30
С. 24
D. 2
7. Five children--Myra, Esmond, Yolanda, Carlos, Lin--are playing a game of hide-and-
go-seek. Myra counts to 10 and the other four children each go to hide in one of the
rooms of the house. If there are 7 rooms that the children could hide in, and each hide
in a different room, how many ways can the children hide?
A. 5,040
В. 2,520
С. 840
D. 210
8. How many ways can the letters of the word BOTTLES be arranged such that both
vowels are at the end?
A. 60
В. 120
С. 720
D. 1,440
9. Among 5 girls in a group, exactly two of them are wearing red shirts. How many ways
are there to seat all 5 girls in a row such that the two girls wearing red shirts are not
sitting adjacent to each other?
A. 12
В. 120
С. 24
D. 72
10. In an ice cream shop, there are eight toppings to choose from. The eight toppings are
arranged in a round revolving tray. How many ways can these toppings be arranged?
A. 5040
В. 10080
С. 2520
D. 5020
Transcribed Image Text:Let's Evaluate Directions: Choose the letter of the correct answer. Write the chosen letter on a separate sheet of paper. 1. The digits 5, 6, 7, and 4 are to be arranged to form a 7-digit integer. How many different integers can be formed? A. 5,674 В. 16,384 C. 840 D. 24 2. In how many ways can the letters of the word REFERENCE be arranged? A. 362,880 B. 181,440 С. 7,560 D. 15,120 3. In how many ways can the letters of the word MATHEMATICS be arranged? B. 39,916.800 A. 6,652,800 C. 4,989,600 D. 55,400 4. A mathematician, a physicist, and an engineer walk into a bar. If there are 3 seats available at the bar, how many ways are there for the mathematician, physicist, and engineer to seat themselves? A. 6 В. 4 С. 1 D. 0 11 5. The mathematician, physicist, engineer, and computer scientist decided to move from the bar to a (circular) table. They file to the table, staying in order as they sit down, and wind up seated as shown below. Engineer Computer Scientist Physicist Mathematician How many different seating arrangements at the bar will lead to the seating arrangement around the table in the image above? A. 0 В. 1 С. 4 D. 6 6. Six friends Andy, Bandy, Candy, Dandy, Endy and Fandy want to form a club. They decide that there will be 1 president, 1 secretary and 4 ordinary members. How many ways can they organize this club? A. 720 В. 30 С. 24 D. 2 7. Five children--Myra, Esmond, Yolanda, Carlos, Lin--are playing a game of hide-and- go-seek. Myra counts to 10 and the other four children each go to hide in one of the rooms of the house. If there are 7 rooms that the children could hide in, and each hide in a different room, how many ways can the children hide? A. 5,040 В. 2,520 С. 840 D. 210 8. How many ways can the letters of the word BOTTLES be arranged such that both vowels are at the end? A. 60 В. 120 С. 720 D. 1,440 9. Among 5 girls in a group, exactly two of them are wearing red shirts. How many ways are there to seat all 5 girls in a row such that the two girls wearing red shirts are not sitting adjacent to each other? A. 12 В. 120 С. 24 D. 72 10. In an ice cream shop, there are eight toppings to choose from. The eight toppings are arranged in a round revolving tray. How many ways can these toppings be arranged? A. 5040 В. 10080 С. 2520 D. 5020
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