Permutations and Combinations MDM 4U: Mathematics of Data
Management Unit: Counting and Probability By: Mr. Allison and Mr.
Panchbhaya
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Specific Expectations Learning Goals Strand 2.1 Recognize the
use of permutations and combinations as counting techniques with
advantages over other counting techniques Strand 2.2 Solve simple
problems using techniques for counting permutations and
combinations, where all objects are distinct Make connections
between, and learn to calculate various permutations and
combinations Learn to behave in class
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Agenda of the Day Probability Video Review Worksheet Game show
Activity
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How many combinations would it take for the tire to attach
itself back to the car?
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Real Life Examples Video game designers to assign appropriate
scoring values Engineering new products tested rigorously to
determine how well they work Allotting numbers for: Credit card
numbers Cell phone numbers Car plate numbers Lottery
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Factorials The product of all positive integers less than equal
or equal to n n! = n x (n 1) x (n 2) x x 2 x 1 5! =5 x 4 x 3 x 2 x
1 = 120
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Permutations
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Combinations Collection of chosen objects for which order does
not matter
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Speed Round: The sports apparel store at the mall is having a
sale. Each customer may choose exactly two items from the list, and
purchase them both. The trick is that each 2-item special must have
two different items (for example, they may not purchase two
T-shirts at the same time). What are all the different combinations
that can be made by choosing exactly two items?
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15 combinations are possible
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Q How many combinations are made if you were purchasing three
items instead of two?
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1. A club of 15 members choose a president, a secretary, and a
treasurer in A.455 ways B.6 ways C.2730 ways
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2. The number of debate teams formed of 6 students out of 10
is: A.151200 B.210 C.720
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3. A student has to answer 6 questions out of 12 in an exam.
The first two questions are obligatory. The student has: A.5040
B.210 C.720
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4. From a group of 7 men and 6 women, five persons are to be
selected to form a committee so that at least 3 men are there on
the committee. In how many ways can it be done. A.564 B.645 C.735
D.756 E.None of the above
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5. In how many different ways can the letters of the word
LEADING be arranged in such a way that the vowels A.360 B.480 C.720
D.5040 E.None of the above
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6. How many permutations of 4 different letters are there,
chosen from the twenty six letters of the alphabet (repetition is
not allowed)?
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Answer The number of permutations of 4 digits chosen from 26 is
26 P 4 = 26 25 24 23 = 358,800
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How many paths are there to the top of the board?
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Answer
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How many 4 digit numbers can be made using 0-7 with no repeated
digits allowed? a)5040 b)4536 c)2688 d)1470
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Answer = 7x7x6x5 = 1470 First digit of a number can not be
0
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No postal code in Canada can begin with the letters
D,F,I,O,Q,U, but repeated letters are allowed and any digit is
allowed. How many postal codes are possible in Canada? a)11,657,890
b)13,520,000 c)14,280,000 d)12,240,000
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Answer = 20x10x26x10x26x10 = 13,520,000 20 choices for the
first letter (26 - 6 that cannot be chosen. 10 choices for the
digit (0-9). 26 choices for the 3 position (2 nd letter) then 10
choice for the 4th position Then 26 and 10 since you can again
repeat numbers and letters.
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Using digits 0 9, how many 4 digit numbers are evenly divisible
by 5 with repeated digits allowed? a)1400 b)1600 c)1800 d)1500
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Answer 9 10 10 2 = 1800 First # cant be 0 Last # has to be 5 or
0
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How many ways can you arrange the letters in the word REDCOATS
if it must start with a vowel a)15,120 b)14,840 c)15,620
d)40,320
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Answer 3* 7 6 5 4 3 2 1 = 15,120 EOA are your 3 choices
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How many groups of 3 toys can a child choose to take on a
vacation from a toy box containing 11 toys? a)990 b)1331 c)165
d)286
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Answer
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If you have a standard deck of cards how many different hands
exists of 5 cards a)2,598,960 b)3,819,816 c)270,725
d)311,875,200
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Answer
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The game of euchre uses only 24 cards from a standard deck. How
many different 5 card euchre hands are possible? a)7,962,624
b)42,504 c)5,100,480 d)98,280
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Answer
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Solve for n 3( n P 4 ) = n-1 P 5 a)8 b)10 c)2 d)5
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Answer
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How many ways can 3 girls and three boys sit in a row if boys
and girls must alternate?
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Answer
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Laura has lost Jordans phone number. All she can remember is
that it did not contain a 0 or 1 in the first three digits. How
many 7 digit #s are possible
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Answer = 8 x 8 x 8 x 10 x 10 x 10 x 10 = 5,120,000
