Published on 2 Aug 2020

School

Department

Course

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

"

❍

7❍Bc

#C

#

❳❳Cc

!

❅❅Ac

"B

10#C

#

❳

3x❳Cc

"

❍❍Bc

x#C

#

❳

0❳Cc

A1.1

mark Find n(B∩C).

A:7 B:10 C:17 D:22 E:cannotbedetermined

A2.1

mark Find n(A∪C).

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 diﬀerent groups of people might be at Julie’s cottageonthelongweekend?

A:2

6B:2

7−1C:6

2D:7

2−1E: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

diﬀerent 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!

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!(n−k)! C:!n

k"=!n

n−k"

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 diﬀerent ways might the 10

silver dollars have been distributed among the 5 children after all of the coins had been

found?

## 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.