Name:    Permutations and Combinations

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

\What is:

6!
3!2!

 a. 6! 6! b. 60 c. 6!5! d. 6

2.

What is:

96!
93!

 a. 857,280 b. 3! c. It can be calculated, but my calculator can’t do it. d. It’s impossible to calculate.

3.

What is:

26!
(26-2)!

 a. 605 b. 26!  26! - 2! c. 26 x 25

4.

What is:

16!
4!3!6!
 a. 3! b. 16! 13! c. 201,801,600 d. 16! 72!

5.

Which of the following formulas could contain counting techniques intended to stop elements from moving (i.e. being sequenced or ordered)?

 a. 16!  4!3!6! b. 26 x 26 x 26 c. 13C3 x 13C7   x  4P2 d. None of the above

6.

Which of the following questions does not require the nCr or nPr formulas?
 a. How many seven card hands consisting of four cards of one suit, and three of another. b. The number of unique groups of diners if you were to invite 3 of your 11 friends out for a double date. c. The number of ways of ordering six of ten textbooks on a shelf. d. The number of locker “combinations” (which are actually sequences) on a ‘spin-dial’ pad lock.

7.

Which of the following is a true statement about pascal’s triangle/combination patterns?
 a. Combinations and rows of pascal’s triangle are symetrical. b. The number at the very left in a row of pascal’s triangle indicates the row number. c. If the row number in pascal’s triangle is n, then there are groups of n different sizes that can be formed in that row (i.e. with n elements). d. The total number of unique groups of all  sizes with n elements is 2(n-1)

8.

What is:

76! - 74!
73!
 a. 3! - 1! b. 2!  73! c. 76P3 - 74 d. This can’t be calculated.

9.

What is:

47P3
 a. 47!   3! b. 45 x 46 x 44 c. 47! 44 d. 47!   (47-3)!

10.

How many ways can the letters of this word be rearranged?

MISSISSAUGA
 a. 11! b. 11P11 c. 11!     4! + 2! + 2! d. 11!  4!2!2! e. 11!   8!

11.

Take the following question:

The Greek alphabet contains 24 letters.  How many different Greek-letter code names can be formed using either two or three letters?

Which counting technique must you use?

 a. Combinations and sum rule b. Permutations and repeated elements c. Combinations, identicle elements, sum rule d. Permutations, repetition of elements, sum rule with cases

12.

Take the following question:

Sophie has picked up her binders for the seven courses she will study this year.  In how many ways can she arrange them on her bookshelf if she wants to keep the Data Management and Calculus binders appart?

Which counting technique(s) must you use?

 a. Direct method, permutuations, identicle elements/no movement b. Indirect method, permutations, no repeated elements c. Combinations, identicle elements, sum rule d. Permutations, repetition of elements, product rule

13.

Take the following question:

You are thinking of having a party at your house. If you have 12 friends, how many different groups can you have over to your house if you want at least two friends to join you for the evening?

Which counting technique(s) should you use?

 a. Direct method, permutuations, identicle elements/no movement b. Indirect method, permutations, no repeated elements c. Combinations, repetition of elements, sum rule d. Combinations, indirect method, pascal’s triangle patterns

14.

Take the following question:

A project team of 6 students is to be formed from a class of 30. Pierre, Gregory, and Miguel are students in this class. How many of the teams would include these three students?

Which counting technique(s) should you use?

 a. Direct method, permutuations, identicle elements/no movement b. Indirect method, permutations, no repeated elements c. Direct method, combinations, no repetition of elements, product rule d. Combinations, indirect method, sum rule

15.

Take the following question:

A project team of 6 students is to be formed from a class of 30. Pierre, Gregory, and Miguel are students in this class. How many of the teams would include at least one of these three students?

Which counting technique(s) should you use?

 a. Direct method, permutuations, identicle elements/no movement, sum separate cases b. Combinations, indirect method, no repeated elements, product rule c. Indirect method, permutations, no repeated elements d. Combinations, direct method, sum rule, separate cases e. Direct method, combinations, no repetition of elements, product rule

16.

7C3 is the same as:
 a. 7 x 6 x 5 ÷ 6 b. 7!     (7-4)!3! c. 7P4 ÷ 4! d. All of these are correct.

17.

Why is 9P3 is the same as 9C3 x 3! ?
 a. This is a trick question. They are not the same. The formula for combinations is not related to the formula for permutations. b. This is because there are more groups when you have 8 elements than there are arrangements of 3 things. c. You must multiple the number of groups by the number of elements in the group to find the number of arrangements the elements of the group can make. d. Every group of n elements can be arranged n! ways.

18.

What is the number in the second position of the 200th row of pascal’s triangle?
 a. 1 b. 201 c. 200 d. 2200 e. 0 f. 200 x 199 ÷ 2