Choose the correct answer with your solution.

1. When asked "How many ways can you arrange r number of objects from n objects?", we are actually asked to count using which counting technique? *

a. Fundamental Counting Principle

b. Permutation with replacement

c. Combination

d. Permutation

2. When asked "How many ways can you select r number of objects from n objects?", we are actually asked to count using which counting technique? *

a. Combination

b. Fundamental Counting Principle

c. Permutation

d. Permutation with replacement

3. When asked "How many ways can you do aa set of activities in sequence?", we are actually asked to count using which counting technique? *

a. Fundamental Counting Principle

b. Combination

c. Permutation

d. Permutation with replacement

4. How many ways can we select a consonant from the letters of the English alphabet? *

25,200

5

21

65,780

5. Given 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? Which type of counting technique is most appropriate to count the total number of words? *

a combination of at least two counting techniques

permutation

fundamental counting principle

combination

6. Given 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?*

210

2,520

25,200

302,400

7. A basketball team is composed of 10 players. How many different selections are there if we are going to select a 5-member starting line-up and a team captain?

10P6

10C1 9C5

10P1 9P5

10C6

8. A basketball team is composed of 10 players. How many different selections are there if we are going to select a 5-member starting line-up and a team captain?

30,240

1,260

151,200

210

9. In the question "How many ways can 10 persons sit in a row of chairs if two of them always sit together?", which of the following describes the best approach to answering the problem?

Treat the 10 people as though they are 9 objects to be arranged multiplied by the permutation of the collective.

Treat the 10 people as though they are 8 objects to be arranged multiplied by the permutation of the collective.

Treat the 10 people as though they are 9 objects to be arranged.

Treat the 10 people as though they are 8 objects to be arranged.

10. How many ways can 10 persons sit in a row of chairs if two of them always sit together?

362,880

725,760

40,320

80,640

11. In the question "How many ways can 10 persons sit in a round table if two of them always sit together?", which of the following describes the best approach to answering the problem?

Treat the 10 people as though they are 9 objects to be arranged.

Treat the 10 people as though they are 8 objects to be arranged.

Treat the 10 people as though they are 9 objects to be arranged multiplied by the permutation of the collective.

Treat the 10 people as though they are 8 objects to be arranged multiplied by the permutation of the collective.

12. How many ways can 10 persons sit in a round table if two of them always sit together?

80,640

725,760

362,880

40,320

13. If a license plate pattern is LLL NNNN where L is a letter and N is a number digit, how many possible license plates can be issued?

88,583,040

156,000,000

78,624,000

175,760,000

14. The question "How many possible iterations are there for the letters in the word Mississippi?" is a question of

78,624,000

175,760,000

156,000,000

88,583,040

15. The question "How many possible iterations are there for the letters in the word Mississippi?" is a question of

getting the linear permutation

getting the permutation with replacement

getting the permutation with indistinguishable elements

getting the permutation without replacement

16. How many possible iterations are there for the letters in the word Mississippi?

11!/(4! 2!)

34,650

11!/6!

40,320

17. How many possible winning numbers are there in a 6/45 lottery?

45 44 43 42 41 40

45P6

6

8,145,060

18. In the question "How many 3-digit numbers can be formed from the set of decimal digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, if the numbers formed are all even numbers and repetition of digits is not allowed?", which place value must be filled in first?

hundreds place

tens place

any of the three place values

ones place

19. How many 3-digit numbers can be formed from the set of decimal digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, if the numbers formed are all even numbers and repetition of digits is not allowed?

328

360

405

720

20. A box contains 5 red balls, 4 green balls, and 7 blue balls. How many ways can we pick 2 balls with different colors?

240

120

83

360

21. On a typical keyboard, there are 26 small cap letters, 26 uppercase letters, 10 decimal digits, and 33 special characters. How many possible passwords 9 characters long can be generated using these options on the keyboard if a character can only be used once?

95!

95P9

86!

95C9