Name___________________________________
Create the boxes for each question
Multiplication Principle
A computer password consists of any five capital letters from the ordinary English alphabet (A through Z).
1. How many different passwords are possible?
A) 25
B) 265
C) 26 × 25 × 24 × 23 × 22
D) 26 × 5
E) none of these
2. How many different passwords have no repeated letters?
A) 265
B) 26 × 25 × 24 × 23 × 22
C) 26 × 5
D) 25
E) none of these
3. How many different passwords start with the letter Z?
A) 254
B) 265 − 1
C) 264
D) 26 × 25
E) none of these
4. How many different passwords start with the letter Z and end with the letter W?
A) 26 × 25 ×243 .
B) 263
C) 243
D) 245
E) none of these
A license plate consists of any five capital letters from the ordinary English alphabet (A through Z) except for the
letters O, I, and Q.
5. How many of the license plates start with the letter Z?
A) 234
B) 23 × 22 × 21 ×20
C) 235 − 1
D) 225
E) none of these
6. How many of the license plates start with the letter Z and end with the letter W?
A) 213
B) 23 × 22 × 213
C) 233
D) 215
E) none of these
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7. How many of the license plates begin with the word MATH?
A) 224
B) 23
C) 234 × 22
D) 23 × 224
E) none of these
A computer password is made up of five characters. Each character can be a capital letter (A through Z) or a
digit (0 through 9).
8. How many different such computer passwords are there?
A) 365
B) 536
C) 36 × 5
D) 265 + 105
E) none of these
9. How many passwords do not start with the digit 0?
A) 355
B) 364
C) 365 − 1
D) 35 × 364
E) none of these
10. How many passwords start with a digit?
A) 10 × 354
B) 364
C) 10 × 264
D) 10 × 364
E) none of these
11. How many passwords consist entirely of letters?
A) 265
B) 26 × 25 × 24 × 23 × 22
C) 26 × 5
D) 526
E) none of these
12. How many passwords have four letters and only one digit?
A) 26 × 25 × 24 × 23 × 10
B) 5 × 264 × 10
C) 264 × 10
D) 4 × 26 × 10
E) none of these
13. How many passwords have three letters and two digits?
A) 26 × 25 × 24 × 10 × 9
B) 3 × 263 × 102
C) 10 × 263 × 102
D) 263 × 102
E) none of these
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Tasmanian automobile licence plates consist of three capital letters (A through Z) followed by three digits (0
through 9).
14. How many different Tasmanian license plates are possible?
A) 263 × 103
B) 366
C) 263 + 103
D) (26 × 3) + (10 × 3)
E) none of these
15. How many Tasmanian license plates end with a 1?
A) 263 × 102
B) 263 × 103 − 1
C) 263 × 103
D) 262 × 103
E) none of these
16. How many Tasmanian license plates start with the word ZOO?
A) 1000
B) 100
C) 1
D) 10
E) none of these
Tasmanian automobile license plates consist of four capital letters (A through Z) followed by three digits (0
through 9).
17. How many different Tasmanian license plates are possible?
A) 367
B) (26 × 4) + (10 × 3)
C) 264 × 103
D) 264 + 103
E) none of these
18. How many Tasmanian license plates end with '66'?
A) 264 × 10
B) 264 × 103
C) 264 × 103 − 1
D) ) 262 × 103
E) none of these
19. How many Tasmanian license plates start with the word MATH?
A) 100
B) 1000
C) 10
D) 1
E) none of these
20. How many Tasmanian license plates start with the word ADD?
A) 2600
B) 26,000
C) 1000
D) 1
E) none of these
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A computer password is made up of four characters. Each character can be a capital letter (A through Z), a
lowercase letter (a through z) or a digit (0 through 9).
21. How many different such computer passwords are there?
A) 462
B) 2 × 264 + 104
C) 62 × 4
D) 624
E) none of these
22. How many passwords do not start with the digit 0?
A) 614
B) 624 − 1
C) 61 × 623
D) 623
E) none of these
23. How many passwords start with a lowercase letter?
A) 26 × 363
B) 26 × 623
C) 363
D) 26 × 364
E) none of these
24. How many passwords consist entirely of letters?
A) 52 × 4
B) 524
C) 452
D) 52 × 51 ×50 × 49
E) none of these
25. How many passwords have 3 letters (uppercase or lowercase) and only one digit?
A) 4 × 52× 10
B) 52 × 51 × 50 × 10
C) 4 × 523 × 10
D) 523 × 10
E) none of these
26. How many passwords do not contain the uppercase letter O, the lowercase o, or the number 0?
A) 59 × 58 × 57 ×56
B) 62 × 25 × 25 × 9
C) 624 − 3
D) 594
E) none of these
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27. How many passwords have 2 letters (uppercase or lowercase) and 2 digits?
A) 522 × 102
B) 2 × 522 × 102
C) 6 × 522 × 102
D) 52 × 51 × 10 × 9
E) none of these
A French restaurant offers a menu consisting of 5 different appetizers, 3 different salads, 2 different soups, 7
different main courses, and 3 different desserts. The restaurant offers different combinations of "fixed price
dinners" on different days of the week.
28. On Monday through Thursday, the "fixed price dinner" consists of a choice of appetizer, a soup, a main course,
and a dessert. Assuming you don't pass on any of these, how many different "fixed price dinners" are possible
on these days?
A) 42
B) 17
C) 70
D) 210
E) none of these
29. On Fridays and Saturdays, the "fixed price dinner" consists of a choice of appetizer, a choice of either soup or
salad, a main course, and a dessert. Assuming you don't pass on any of these, how many different "fixed price
dinners" are possible on Fridays and Saturdays?
A) 20
B) 630
C) 21
D) 525
E) none of these
30. On Sundays, the "fixed price dinner" consists of a main course, a dessert, and any two of the other three types
of items (i.e., appetizer and soup, or appetizer and salad, or soup and salad). Assuming you don't pass on any
of these, how many "fixed price dinners" are possible on Sundays?
A) 30
B) 420
C) 651
D) 5880
E) none of these
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A French restaurant offers a menu consisting of 4 different appetizers, 5 different salads, 3 different soups, 7
different main courses, and 8 different desserts. The restaurant offers different combinations of "fixed price
dinners" on different days of the week.
31. On Monday through Thursday, the "fixed price dinner" consists of a choice of appetizer, a soup, a main course,
and a dessert. Assuming you don't pass on any of these, how many different "fixed price dinners" are possible
on these days?
A) 68
B) 392
C) 22
D) 672
E) none of these
32. On Fridays and Saturdays, the "fixed price dinner" consists of a choice of appetizer, a choice of either soup or
salad, a main course, and a dessert. Assuming you don't pass on any of these, how many different "fixed price
dinners" are possible on Fridays and Saturdays?
A) 1792
B) 180
C) 3360
D) 672
E) none of these
33. On Sundays, the "fixed price dinner" consists of a main course, a dessert, and any two of the other three types
of items (i.e., appetizer and soup, or appetizer and salad, or soup and salad). Assuming you don't pass on any
of these, how many "fixed price dinners" are possible on Sundays?
A) 2632
B) 2688
C) 1344
D) 3360
E) none of these
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1) B
2) B
3) C
4) B
5) A
6) C
7) B
8) A
9) D
10) D
11) A
12) B
13) C
14) A
15) A
16) A
17) C
18) A
19) B
20) B
21) D
22) C
23) B
24) B
25) C
26) D
27) C
28) D
29) D
30) C
31) D
32) A
33) A
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