Solutions found at the end of this file.

1) Certain government employees are classified into 6 categories according to age
and 4 categories according to marital status.
In how many ways can 1 of these employees be classified?

(2)

2) Determine whether each of these statements is true or false.

a)	b) 3! + 2! = 5!
c)	d) 3! + 0! = 7

(4)

3) The 5 finalists in the Miss Arizona contest are Ms. Cochise (C), Ms. Gila (G),
Ms. Pima (P), Ms. Maricopa (M), and Ms. Yuma (Y).
Make a tree diagram to show the different ways in which the judges can choose
the winner and the first runner-up.

(2)

4) What is the probability of rolling a 5 with a pair of balanced dice?

(4)

5) In how many ways can you arrange 6 books on a shelf?

(2)

6) A test consists of 10 questions, each with 5 different possible answers.
In how many ways can you choose 1 answer for each of the 10 questions?

(3)

7) In how many ways can 3 reporters known as A, B and C, divide up 10 assignments
so that A will get 2, B will get 5 and C will get 3?

(3)

8) A local theatre has scheduled 6 concerts, 8 lectures and 5 plays.
In how many different ways can you choose to attend:

a) 1 concert and 1 play?

b) 1 concert, 1 lecture and 1 play?

(4)

9) If 756 or 1200 letters mailed by a company were delivered within 48 hours,
estimate the probability that any one letter mailed by the company will be
delivered within 48 hours.

(2)

Solutions

1) Ways to catergorize = 6 $ 4 = 24

2)

a) T

b) F

c) F

d) T

3)

4) ways to roll 5 are (1, 4) (2, 3) (3, 2) and (4, 1) = 4 of 36 possibilities,
so P(5) = 4/36 = 1/9

5) 6! = 720 ways

6) 5 ¹⁰ = 9, 765, 625 ways to choose an answer.

7) ₁₀ C ₂ $ ₈ C ₅ $ ₃ C ₂ = 2,520 ways

8) a) 1 concert and 1 play = ₆ C ₁ $ ₅ C ₁ = 30 ways
b) ₆ C ₁ $ ₈ C ₁ $ ₅ C ₁ = 6 $ 8 $ 5 = 240 ways

9) Probability letter is delivered within 48 hours = 756/1200 = 0.63

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