Let's EvaluateDirections: Choose the letter of the correct answer. Write the chosen letter on a separate sheetof paper.1. The digits 5, 6, 7, and 4 are to be arranged to form a 7-digit integer. How many differentintegers can be formed?A. 5,674В. 16,384C. 840D. 242. In how many ways can the letters of the word REFERENCE be arranged?A. 362,880B. 181,440С. 7,560D. 15,1203. In how many ways can the letters of the word MATHEMATICS be arranged?B. 39,916.800A. 6,652,800C. 4,989,600D. 55,4004. A mathematician, a physicist, and an engineer walk into a bar. If there are 3 seatsavailable at the bar, how many ways are there for the mathematician, physicist, andengineer to seat themselves?A. 6В. 4С. 1D. 0115. The mathematician, physicist, engineer, and computer scientist decided to move fromthe bar to a (circular) table. They file to the table, staying in order as they sit down, andwind up seated as shown below.EngineerComputerScientistPhysicistMathematicianHow many different seating arrangements at the bar will lead to the seatingarrangement around the table in the image above?A. 0В. 1С. 4D. 66. Six friends Andy, Bandy, Candy, Dandy, Endy and Fandy want to form a club. Theydecide that there will be 1 president, 1 secretary and 4 ordinary members. How manyways can they organize this club?A. 720В. 30С. 24D. 27. 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 therooms of the house. If there are 7 rooms that the children could hide in, and each hidein a different room, how many ways can the children hide?A. 5,040В. 2,520С. 840D. 2108. How many ways can the letters of the word BOTTLES be arranged such that bothvowels are at the end?A. 60В. 120С. 720D. 1,4409. Among 5 girls in a group, exactly two of them are wearing red shirts. How many waysare there to seat all 5 girls in a row such that the two girls wearing red shirts are notsitting adjacent to each other?A. 12В. 120С. 24D. 7210. In an ice cream shop, there are eight toppings to choose from. The eight toppings arearranged in a round revolving tray. How many ways can these toppings be arranged?A. 5040В. 10080С. 2520D. 5020

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Description: Let's EvaluateDirections: Choose the letter of the correct answer. Write the chosen letter on a separate sheetof paper.1. The digits 5, 6, 7, and 4 are to be arranged to form a 7-digit integer. How many differentintegers can be formed?A. 5,674В. 16,

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Math

Advanced Math

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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

Topic Video

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

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