Mathematics 1228A/B Final: 1228 Final exam 2008 (3)

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Published on 2 Aug 2020
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Professor
Wednesday, April 16, 2008
Page 1 CODE 111 Mathematics 028b/031
Final Examination
PART A (35 marks)
Use the counting tree shown here for questions A1 and A2:
45
15!A
"B
7#C
#
Cc
"
7Bc
#C
#
Cc
!
Ac
"B
10#C
#
3xCc
"
Bc
x#C
#
0Cc
A1.1
mark Find n(BC).
A:7 B:10 C:17 D:22 E:cannotbedetermined
A2.1
mark Find n(AC).
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mark
A:7 B:30 C:37 D:45 E:cannotbedetermined
A3.1
mark Julie has invited 6 friends to her cottage for the Victoria Daylongweekendnextmonth,
but she doesn’t yet know how many will actually come. Julie will go to the cottage even
if none of her friends will be there. No one other than Julie andherfriendswillbethere.
How many dierent groups of people might be at Julie’s cottageonthelongweekend?
A:2
6B:2
71C:6
2D:7
21E:7!
A4.1
mark In how many distinct ways can each of 5 children choose a red crayon, a yellow crayon
or an orange crayon? (There are at least 10 identical crayons of each colour. Each child
chooses exactly 1 crayon, of whichever colour he/she wants.)
A:5
3B:3
5C:!5
3"D:5!
2! E:!34
30"
A5.1
mark In how many distinct ways can 5 drawings of flowers be arranged in a row if there are 3
dierent pictures of red flowers, 1 picture of an orange flower and 1 picture of a yellow
flower, and all the pictures of red flowers must be together in the row?
A:5!3! B:5!
2! C:3!1!1! D:3!2! E:3!3!
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Mathematics 028b/031
Final Examination CODE 111 Wednesday, April 16, 2008
Page 2
A6.1
mark In how many distinct ways can 5 children sit in a circle if 2 of the children, Sally and
Karen, must be side-by-side?
A:4! B:4!×2C:3! D:3!×2E:5!
A7.1
mark Which one of the following relationships is not always true?
A:!n
1"=nB:!n
k"=n!
k!(nk)! C:!n
k"=!n
nk"
D:!n
n"=1 E:!2n
k"=2×!n
k"
A8.1
mark The 6 members of a club are going to divide themselves up into 3 teams, with 2 people on
each team, and then a team captain will be chosen for each team.Inhowmanydistinct
ways can this be done?
A:15 B:30 C:90 D:120 E:240
A9.1
mark Ten identical silver dollars were hidden in a ro om. Five children hunted for the silver
dollars, each keeping the coins he or she found. In how many dierent ways might the 10
silver dollars have been distributed among the 5 children after all of the coins had been
found?
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Document Summary

Use the counting tree shown here for questions a1 and a2: Julie has invited 6 friends to her cottage for the victoria day long weekend next month, but she doesn"t yet know how many will actually come. Julie will go to the cottage even if none of her friends will be there. No one other than julie and her friends will be there. In how many distinct ways can each of 5 children choose a red crayon, a yellow crayon or an orange crayon? (there are at least 10 identical crayons of each colour. Each child chooses exactly 1 crayon, of whichever colour he/she wants. ) In how many distinct ways can 5 drawings of owers be arranged in a row if there are 3 di erent pictures of red owers, 1 picture of an orange ower and 1 picture of a yellow.

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