Chapter 5 - Combinations and the Binomial Theorem
Chapter 4 - Permutations and Organized Counting
Chapter 4 - Practice
1. An all-star baseball team has a roster of 7 pitchers and 3 catchers. How many pairs of pitcher and catcher can the manager select from the roster?
[pic]
2. New houses in a sub-division are available in three-, four- and five-bedroom models, which may be built with six different exterior finishes, with or without a swimming pool. How many distinct selections can be made by the customer?
[pic]
3. Write the number of arrangements of the letters of the word KETCHUP using factorial notation.
[pic]
4. In how many ways can a chairman, treasure and secretary be selected from a Board Of Directors with eight members?
[pic]
5. If 1000 people enter a contest in which there is a first prize, a second prize and a third prize, in how many ways could the prizes be given?
[pic]
6. Emilio has picked up his textbooks for the 7 courses he will study this year. In how many ways can he arrange them on his bookshelf if he wants to keep the French and German texts side-by-side?
[pic]
7. Find the number of ways of arranging the letters of MATCHING if
a) There are no restrictions.
b) The first letter must be M.
c) The odd-numbered positions must remain the same.
d) The arrangement must end with NG.
a) [pic] b) [pic] c) [pic]
d) [pic]
8. A man bought two vanilla ice cream cones, three chocolate cones, four strawberry cones and one pistachio cone for his ten children. In how many ways can he distribute the flavours among his children? (Assume order matters)
[pic]
9. Emily’s minor soccer team played a total of 14 games in the season. Their record was eight wins, four losses, and two ties. In how many orders could this have happened?
[pic]
10. In how many ways can 11 players be seated on the team bench so that Joey and Jill are not seated next to eachother?
Seated next to eachother: [pic]
Not next to eachother: [pic]
11. Determine the sum of the terms in the 14th row of Pascal’s Triangle
[pic]
12. Determine[pic].
[pic]
13. Determine the number of possible routes from A to B if you only travel south or east.
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A
B
1
1
1
1
1
1
2
3
4
5
6
21
15
10
6
3
1
56
35
20
10
4
1
126
70
35
15
5
1
OR [pic]
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