Extension Activity / Bonus Questions - Math with Mr. K.
Grade 12 621A Math Chapter 4: (STUDY)
Sections: 4.1 to 4.6 notes
Formulas:
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General Knowledge
a) 0! = f) Express 3 x 2 x 1 in factorial notation.
b) Evaluate [pic] g) Evaluate [pic]=
c) Evaluate [pic] h) Evaluate [pic]
d) Does [pic] i) Does [pic]
e) Write the following expressions using factorial notation
i) [pic] ii) [pic]
Problem Set
The problems are in no particular order. It is important to be able to recognize what type of method is needed for a solution.
REMEMBER: Permutations – Order is Important
Combinations – Order is NOT Important
Section 4.1 FCP
1. A restaurant offers 6 different lunch entrees, with a choice of 3 different types of potatoes, 3 different types of salads, and 5 different beverages. How many different lunches can be ordered?
2. There are 12 teams in a tournament. The top three teams win gold, silver, and bronze medals. In
how many different ways could the medals be awarded to the teams?
3. In how many ways can 5 students be selected from a class containing 30 students?
4. Determine the number of different ways that 9 bikes can be locked in a bike rack.
5. How many ways can 3 suckers, 2 chip bags and 2 chocolate bars be distributed among 7 children?
6. How many odd 3 digit whole numbers are there?
7. Determine the number of permutations of all the letters in each word.
a) Mathematician b) BASEBALL c) MISSISSIPPI
8. In each case, how many 2 digit whole numbers can be formed using the digits 1, 2, 3, 4, and 5?
a) Repetitions are not allowed.
b) Repetitions are allowed.
9. How many 5 card poker hands have exactly 3 face cards?
10. a) How many permutations can be formed using all the letters of the word
MUSCLE?
b) How many 3-letter permutations can be formed from the letters of the word
MUSCLE?
11. Sam sells hockey equipment as a part time job. He has four different types of shin
guards, 6 different pairs of skates, 7 types of hickey sticks and 3 different types of
helmets. How many different outfits are there (assume outfit includes shin guard,
skates, stick and helmet)?
12. Mrs. Jackson class of 18 students all submitted projects for a science fair. The principal asked Mrs.
Jackson to prepare a display for the upcoming parent teacher evening.
a) In how many ways can the 8 projects be chosen?
b) In how many ways can the 8 projects be displayed? Express answer in factorial form.
13. How many different paths are there from A to B if only Down and Right travel is permitted?
A A A
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B
B
14. How many different arrangements can be made using all the letters in HOLLYWOOD, if the first
letter must be L and the last letter must be Y?
15. A football stadium has nine gates: four on the north side and five on the south side.
a) In how many ways can you enter and leave the stadium?
b) In how many ways can you enter through a north gate and leave by any gate?
16. In each case, how many even 4 digit # formed. Repetitions allowed
17. A photo album consists of pages that each hold 4 photos. How many arrangements are possible
for the first page of the photo album if a person has 24 photos?
18. Kinkora’s team sells 25 tickets to different people. First draw gets $100, second gets $50 and
third gets $25. How many different ways are there to draw the three winners and nobody can win
more than one prize?
19. A standard deck of 52 playing cards consists of 4 suits (spades, hearts, diamonds, and clubs) of 13
cards each.
a) How many different 6-card hands can be formed?
b) How many different 6-card hands can be formed containing all clubs?
c) How many different 6 card hand can be formed if three of the cards are clubs?
d) How many different 6 card hands can be formed if only one card is black?
e) How many different 6-card hands can be formed containing at least 4 clubs?
20. Neil is creating an 6-character password. Half of the characters will be upper OR
lower case letters, the last 3 characters of the password will be digits from 0 to 9.
Characters will not be use more than once. How many passwords are possible?
21. Radio and TV stations have four character station names. There are 3 choices for the first letter: K, W, and C.
The other characters can be capital letters or numbers from 0 to 9. How many station names are possible?
Repetition of characters are allowed.
22. How many 5 card hands are there with 3 clubs and 2 diamonds? There is no repetition in cards in a
hand and the order doesn’t matter, so we have a combination. Since we want them both to occur at
the same time, we use the fundamental Counting principle.
23. At a child’s birthday party, prizes are awarded for best costume, best craft and best decorated
cookie. In how many different ways can prizes be awarded to 15 guests at the party if
a) the children cannot win more than one prize
b) the children can receive all the prizes.
24. On a 9 question multiple choice test, 4 answers are A, 2 answers are B and 3 answers are C. How
many different answer keys are possible?
25. An environmental committee of 6 people is to be selected from a class with 10 women and 8 men. In
how many ways can a committee be formed if it must contain only women?
26. In how many ways can four girls and three boys be arranged in a row in each situation?
a) A boy must be at each end of the row
b) A girl must sit in the first, third seat and fifth seat
27. In how many ways can 6 people be arranged in a row for a photo shoot?
28. Tina is playing with a tub of building blocks. The tub contains 3 red blocks, 5 blue blocks, 2 yellow blocks, and
4 green blocks. How many different ways can Tina stack the blocks in a single tower in each situation below?
a) No conditions
b) There must be a yellow block at the bottom of the tower and a yellow block at the top of the tower.
29. a) How many ways can a committee of 4 be selected from 15 boys and 10 girls.
b) How many ways can a committee of 4 be selected from 15 boys and 10 girls if there is exactly one girl on the committee.
c) How many ways can a committee of 4 be selected from 15 boys and 10 girls if there is at least one girl on the committee.
30. A map of Canada is to be coloured with a different colour for each province (10) or territory (3).
If 15 colours are available, in how many ways can the map be coloured?
31. a) How many 7 letter arrangements can you make using all the letters L, M, N, O, P, I, and U?
b) Of these, how many begin and end with a vowel?
c) Of these, how many begin with a consonant and end with a vowel?
32. From seven grade 10 students and 4 grade 11 students, a dance committee of 6 is to be formed. In
how many ways can this be done if the committee must have exactly 2 grade 10 students?
33. How many six card hands can be formed that contain exactly 2 spades, and 2 diamonds.
34. Hannah play on a local hockey team. The hockey uniform has:
• Four different sweaters : Blue, White, Grey and Black
• Two different pants: Blue and Grey
a) Draw a tree diagram to determine how many different variations of the uniform the coach can choose from for each game?
b) Confirm your answer using the fundamental counting principle.
35. How many different arrangements are possible if all the letters are used in the word MATHEMATICS, but each
arrangement must begin with a C.
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