©Zarestky
Math 141 Quiz 6 Version A
10/15/2009
NAME:________________________________________
1.
(3 pts) Suppose you buy 10 different canned goods at the grocery store and you want to arrange them in
your pantry. Of the 10 cans, 2 are canned veggies, 3 are canned fruit, and 5 are soup. In how many ways
can you arrange all 10 cans on the bottom shelf by type?
Arrange the types, then arrange the cans of each type.
3! ⋅ 2! ⋅ 3! ⋅ 5! = 8640 ways
2.
(3 pts) At a fruit stand there are 12 cantaloupes, of which 4 are ripe. A sample of 6 cantaloupes is
selected at random. How many samples have exactly 3 ripe cantaloupes?
Out of the 12 total, 4 ripe means 8 are unripe. In the sample of 6, 3 ripe means 3 are unripe.
Choose 3 of the 4 ripe, and 3 of the 8 unripe.
C(4, 3) ⋅ C(8, 3) = 224 samples
3.
(4 pts) 100 students were surveyed regarding their habits before an 8am Math 141 class. Students were
asked if they wake up before 7am (W) and if they drink caffeine before class (C). Use the given
information to label each region of the Venn diagram with the appropriate number of students.
•
•
•
44 students wake up before 7am.
62 students drink caffeine before class.
12 students do neither.
a + b + c + d = 100
a + b = 44
b + c = 62
d = 12
W
a = 26
d = 12
b = 18
C
c = 44