Order Counting Techniques Discussion Assignment

Order Counting Techniques Discussion Assignment

1. How many different meal combinations consisting of one sandwich,

one drink, and one type of chips are possible from a selection of

8 kinds of sandwiches, 5 drinks, and 7 types of chips?

(A) 20

(B) 35

(C) 40

(D) 280

2. A code for a locking briefcase consists of five digits that must be

entered in a definite order. Each of the digits 0 through 9 may be used

in the code, and repetition of digits is allowed. How many different

five-digit codes are possible?

(A) 100,000

(B) 59,049

(C) 30,240

(D) 15,120

3. There are 30 separate candidates for three vice president positions at a

university. Assuming all 30 candidates are qualified to be selected for

any one of the three VP positions, how many different ways can the

positions be filled?

(A) 27,000

(B) 24,360

(C) 4,060

(D) 60

Chapter 6

445 ❯ McGraw-Hill’s 500 Statistics Questions

4. Suppose a high school issues each student a student identification (ID)

number that consists of two letters followed by six digits (0 through 9).

Assuming repetition of letters and digits is not allowed, how many unique

student ID numbers are possible?

(A) 26 9 2 6 ⋅

(B) 26

2

10

6

(C) 26 10 2 6 ⋅

(D) 26 25 10 9 8 7 6 5 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

5. In a certain state, the alphanumeric code for a car license plate consists

of three letters followed by three digits (0 through 9). For that state, how

many different car license plate alphanumeric codes are possible if repetition of digits and letters is allowed?

(A) 366

(B) 26 10 3 3 ⋅

(C) 26 9 3 3 ⋅

(D) 26

3

10

3

6. For the area code 936, how many seven-digit telephone numbers that

begin with 564- are possible if repetition of digits is allowed?

(A) 104

(B) 3 104 ⋅

(C) 10 9 8 7 ⋅ ⋅ ⋅

(D) 107

7. Suppose a code is dialed by means of three disks, each of which is stamped

with 15 letters. How many three-letter codes are possible using the three

disks?

(A) 15C3

(B) 153

(C) 15⋅ ⋅ 14 13

(D) 15 3

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