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MATH 245: QUIZ 5 SOLUTIONS
1)
a) An extreme scenario: It doesn't get any worse than this  you pick 4 reds, 4
blues, and 4 greens. I must get at least 5 balls of the same color by the 13
th
ball.
Answer:
13
.
b) An extreme scenario: You pick the 10 reds, then the 10 blues; the next 5 balls
must be green. You must get at least 5 greens by the 25
th
ball.
Answer:
25
.
2)
I want to count the relevant integers that are divisible by 5, but I need to subtract
the number of those integers that are also divisible by 15.
4999
5
⎢
⎣
⎢
⎥
⎦
⎥
−
4999
15
⎢
⎣
⎢
⎥
⎦
⎥
=
999
−
333
=
666
3)
a) Start with the leftmost position, then do the rightmost position, and then do the
intermediate positions from left to right:
5
V
24
23
22
21
21
C
Product =
26,777,520
b)
The number of strings that begin with a vowel:
5
V
26
26
26
26
26
Product =
5
×
26
5
The number of strings that end with a vowel:
26
26
26
26
26
5
V
Product =
5
×
26
5
However, we are doublecounting the strings that begin and
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 Spring '11
 staff
 Math

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