Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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The number of different ways that 9 bikes can be locked in a bike rack is
A. | 3 628 800 | C. | 40 320 | B. | 20 160 | D. | 362 880 |
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2.
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Evaluate  . A. | 32 432 400 | C. | 6435 | B. | 163 459 296 000 | D. | 259 459 200 |
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3.
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Solve for the variable:  = 252 A. | 15 | C. | 6 | B. |  | D. |  |
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4.
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Evaluate the expression  . A. | 2184 | C. | 794 976 | B. | 87 178 291 200 | D. | 239 500 800 |
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5.
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Rachael has a digital music player that holds 800 songs. She has 1500 songs in
her music library. She decides that her 50 favourite songs must be on the player. Which expression
can be used to calculate the number of ways can she load songs on to the MP3 player so that it is
full?
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6.
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For which of the following terms is a = 55 in the expansion of (x
+ y)11?
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7.
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Prom’s friend gives him a row of Pascal’s triangle and asks which
row it comes from. Prom adds the numbers and obtains a sum of 65 536. Which row do the numbers come
from?
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8.
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How many terms are there in the expansion of  ?
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9.
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A scout troop is arranged in a circle for an opening ceremony. If there are 9
scouts, in how many unique ways can they stand around the circle?
A. | 5040 | C. | 81 | B. | 40 320 | D. | 362 880 |
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10.
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Suppose that 10 non-collinear points are plotted on a plane. Which expression
represents the number of triangles that can be formed using these points?
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Short Answer
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1.
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Sun Eui and Pattie are arguing about the number of ways the letters in
PERMUTATION and COMBINATION can be rearranged. Sun Eui believes that there are more ways to rearrange
PERMUTATION, while Pattie thinks that COMBINATION has more unique arrangements. Which person is
correct?
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2.
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Solve for n:  .
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Problem
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1.
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Expand and simplify:  .
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2.
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On a Saturday, Charlie has to go to the library to study for a few hours, and
then to the school to play a volleyball game. 
a) How many routes are there for Charlie to go from home to the
library if she only moves south and east? b) How many routes are there for her to go from
home to school moving only south and east? c) Assuming Charlie moves south and east going
from home to school and north and west going from school to home, how many routes are there for her
to complete the round trip? d) If Charlie could walk each route from home to school in 40
min, how long would it take her and her 22 classmates to walk all of the routes? Consider only the
route from home to school, not the round trip.
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3.
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Ms. Jackson’s class of 28 students all submitted projects for a recent
math fair. The principal asked Ms. Jackson to prepare a display for the upcoming parent–teacher
evening.
a) In how many ways can 20 of the projects be chosen?
b) The principal
asks to set the 4 regional winners out of the 20 selected near the entrance of the room. In how many
ways can the projects be displayed? Leave your answer in factorial form.
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