Counting & Probability – Unit 1
Review
1. Students can travel to and from school by way of the park, the
library, or the variety store. For example, they can go to school
by way of the park and return by way of the library. Draw a tree
diagram and determine the possible number of routes taken to
and from school on one day.
2. How many three-letter ‘words’ can be formed from the letters of
the word SHORTEN with no letter repeated?
3. In how many ways can the eight members of the board of
directors of Pride International Corp. be seated around the round
table in the board room?
4. At the opening assembly of the school year, the music students
are to perform. The Senior Band knows seven pieces but the
Junior Band knows only two so far, and the students of the Vocal
Music class know three songs. Each group is to perform one
piece.
a. If the Junior Band must play first, followed by the Vocal
Music students, and then the Senior Band, how many
different programs are possible?
b. If the groups may play in any order, how many possible
programs would there be?
5. How many odd four-digit numbers, all of the digits different, can
be formed from the digits 0 to 7, if there must be a 4 in the
number?
6. Five boats of various types (2 of which are sail boats) are to be
docked in the five slips at a small marina.
a. In how many ways can they be docked so that the
powerboat is at the end nearest the boathouse?
b. In how many ways can they be located so that the two
sailboats are at the extreme ends of the marina?
c. In how many ways can they be located so that either the
powerboat is nearest the boathouse or the sailboats are at
the extreme ends?
Answers:
1. 9
6a. 24
2. 210
b. 12
3. 5040
c. 36
4a. 42
b. 252
5. 320
Stewart, J., Kavison, T., Hamilton, O., Laxton, J., Lenz, J. (1988). Finite Mathematics, pg 28. McGraw-Hill Ryerson Limited
Counting & Probability – Unit 1
Review
1. Twelve executives arrive at a meeting. If all shake hands with each other,
how many handshakes occur?
2. Jonathan has six close friends. In how many ways can he invite one or
more of them to dinner?
3. On an exam paper are instructions that, in total, seven questions must be
completed. If ten question are given and the first three questions are
compulsory, how many selections of questions are possible?
4. In how many ways can a school committee of ten be formed if the
committee must include the principal or vice-principal, four teachers from
a staff of 71, and five student council members from the council of 21
students?
5. A package of 20 transistors contains fifteen that are perfect and five that
are defective. In how many ways can five of these transistors be selected
so that at least three are perfect?
Answers:
1. 66
2. 63
3. 35
4. 39,543,601,230
5. 14,378
Stewart, J., Kavison, T., Hamilton, O., Laxton, J., Lenz, J. (1988). Finite Mathematics, pg 66. McGraw-Hill Ryerson Limited