Multiple Choice Identify the choice that best completes the statement or answers
the question.


1.

\What is:
6! 3!2!


2.

What is:
96! 93!
a.  857,280
 b.  3!
 c.  It can be
calculated, but my calculator can’t do it.
 d.  It’s impossible to
calculate.



3.

What is:
26! (262)!
a.  605
 b.  26! 26! 
2!
 c.  26 x 25



4.

What is:
16! 4!3!6!
a.  3!
 b.  16! 13!
 c.  201,801,600
 d.  16!
72!



5.

Which of the following formulas could contain counting techniques intended to
stop elements from moving (i.e. being sequenced or ordered)?
a.  16! 4!3!6!
 b.  26 x 26 x 26
 c.  _{13}C_{3} x _{13}C_{7 }x
_{4}P_{2}  d.  None of the
above



6.

Which of the following questions does not require the _{n}C_{r}
or _{n}P_{r} formulas?
a.  How many seven card hands consisting of four cards of one suit, and three of
another.
 b.  The number of unique groups of diners if you were to invite 3 of your 11 friends out
for a double date.
 c.  The number of ways of ordering six of ten
textbooks on a shelf.
 d.  The number of locker “combinations”
(which are actually sequences) on a ‘spindial’ pad
lock.



7.

Which of the following is a true statement about pascal’s
triangle/combination patterns?
a.  Combinations and rows of pascal’s triangle are
symetrical.
 b.  The number at the very left in a row of pascal’s triangle indicates the row
number.
 c.  If the row number in pascal’s triangle is n, then there are groups of n
different sizes that can be formed in that row (i.e. with n elements).
 d.  The total number of
unique groups of all sizes with n elements is
2^{(n1)}



8.

What is:
76!  74!
73!
a.  3!  1!
 b.  2!
73!
 c.  _{76}P_{3}  74
 d.  This can’t be
calculated.



9.

What is:
_{47}P_{3}
a.  47! 3!  b.  45 x 46 x 44
 c.  47!
44
 d.  47! (473)!



10.

How many ways can the letters of this word be
rearranged?
MISSISSAUGA
a.  11!
 b.  _{11}P_{11}
 c.  11! 4! + 2! +
2!
 d.  11! 4!2!2!
 e.  11!
8!



11.

Take the following question:
The Greek alphabet contains 24
letters. How many different Greekletter code names can be formed using either two or three
letters?
Which counting technique must you use?
a.  Combinations and sum rule
 b.  Permutations and repeated
elements
 c.  Combinations, identicle elements, sum rule
 d.  Permutations,
repetition of elements, sum rule with cases



12.

Take the following question:
Sophie has picked up her binders for the
seven courses she will study this year. In how many ways can she arrange them on her bookshelf
if she wants to keep the Data Management and Calculus binders appart?
Which counting
technique(s) must you use?
a.  Direct method, permutuations, identicle elements/no movement
 b.  Indirect method,
permutations, no repeated elements
 c.  Combinations, identicle elements, sum
rule
 d.  Permutations, repetition of elements, product
rule



13.

Take the following question:
You are thinking of having a party at
your house. If you have 12 friends, how many different groups can you have over to your house if you
want at least two friends to join you for the evening?
Which counting technique(s) should
you use?
a.  Direct method, permutuations, identicle elements/no movement
 b.  Indirect method,
permutations, no repeated elements
 c.  Combinations, repetition of elements, sum
rule
 d.  Combinations, indirect method, pascal’s triangle
patterns



14.

Take the following question:
A project team of 6 students is to be
formed from a class of 30. Pierre, Gregory, and Miguel are students in this class. How many of the
teams would include these three students?
Which counting technique(s) should you
use?
a.  Direct method, permutuations, identicle elements/no movement
 b.  Indirect method,
permutations, no repeated elements
 c.  Direct method, combinations, no repetition of
elements, product rule
 d.  Combinations, indirect method, sum
rule



15.

Take the following question:
A project team of 6 students is to be
formed from a class of 30. Pierre, Gregory, and Miguel are students in this class. How many of the
teams would include at least one of these three students?
Which counting
technique(s) should you use?
a.  Direct method, permutuations, identicle elements/no movement, sum separate
cases
 b. 
Combinations, indirect method, no repeated elements, product rule
 c.  Indirect method, permutations, no repeated elements
 d.  Combinations, direct
method, sum rule, separate cases
 e.  Direct method, combinations, no repetition of
elements, product rule



16.

_{7}C_{3} is the same as:
a.  7 x 6 x 5 ÷ 6
 b. 
7! (74)!3!
 c.  _{7}P_{4} ÷
4!
 d.  All of these are correct.



17.

Why is_{ 9}P_{3} is the same as _{9}C_{3 }x 3!
?
a.  This is a trick question. They are not the same. The formula for combinations is not
related to the formula for permutations.
 b.  This is because there are more groups when you
have 8 elements than there are arrangements of 3 things.
 c.  You must multiple
the number of groups by the number of elements in the group to find the number of arrangements the
elements of the group can make.
 d.  Every group of n elements can be arranged n!
ways.



18.

What is the number in the second position of the 200th row of pascal’s
triangle?
a.  1
 b.  201
 c.  200
 d.  2^{200}  e.  0
 f.  200 x 199 ÷
2

