Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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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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2.
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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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3.
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For a mock United Nations, 6 boys and 7 girls are to be chosen. If there are 12
boys and 9 girls to choose from, how many groups are possible?
A. | 846 720 | C. | 960 | B. | 33 264 | D. | 120 708 403 200 |
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4.
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Determine the coefficient, a, for the term  of the binomial expansion
of  .
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5.
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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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6.
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Which of the following has 30 terms in its binomial expansion?
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7.
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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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8.
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A scout troop is arranged in a circle for an opening ceremony with its leaders.
Assuming there are 7 troop leaders who stand together for the ceremony and 39 scouts in total,
including the troop leaders, in how many unique ways can they be arranged around the circle?
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9.
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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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10.
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The leadership committee at a high school has 4 grade 10 students, 2 grade 11
students, and 6 grade 12 students. This year, 12 grade 10, 8 grade 11, and 10 grade 12 students
applied for the committee. How many ways are there to select the committee?
A. | 2 910 600 | C. | 733 | B. | 100 590 336 000 | D. | 163 136 |
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Short Answer
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1.
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Josie goes to the local submarine sandwich shop. She can choose from 21 types of
sandwiches. There are 3 types of cheese, 8 types of vegetables, and 7 types of sauce. Assuming that
Josie only chooses one type of cheese, one vegetable, and one sauce for her sandwich, how many
choices does she have?
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2.
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Simplify the expression  .
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Problem
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1.
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The chorus of a play has 17 females and 13 males. The director wishes to meet
with 6 of them to discuss the upcoming production.
a) How many selections are
possible?
b) How many selections are possible if the group consists of three females and
three males?
c) One of the male students is named Ajay. How many six-member selections
consisting of Ajay, two other males, and three females are possible?
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2.
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Simplify. a)  b) 
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3.
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Which of the following binomial expansions has the greater coefficient: the 12th
term in the expansion of  or the 8th term in the expansion of  ?
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