Category 4 Arithmetic Meet #5 Worksheet With Answers - 2001 Page 8
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12Solutions to Category 4
Arithmetic
Meet #5, April 2004
1. The event that Hadley has pizza and drinks chocolate
Answers
milk is often refered to as a compound event. We can
multiply the probabilities of the individual events to find
1
1.
the probability of the compound event. Doing so, we get
5
3
1
1
.
×
=
5
3
5
2. 336
3. 56
2. There are 8 possible first place winners. For each of
these eight possible first place winners, we must consider
7 possible second place winners and 6 possible third
place winners. Thus, the photographer would need to
take 8 × 7 × 6 = 336 different pictures. This is known as
a permutation and also calculate as follows:
8!
8 ⋅ 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅1
P
=
=
= 8 ⋅ 7 ⋅ 6 = 336
8
3
(
)
8 − 3
!
5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅1
3. In choosing this group of three from the group of
eight, there is no special significance to being chosen
first, second, or third. In other words, the selection of
Aaron, then Beth, then Cecille is no different than the
selection of Aaron, then Cecille, then Beth, since the
same three people will stay at base camp. If we divide
the 336 from question 2 by the number of different ways
that three people can be arranged, which is 3 × 2 × 1 = 6,
we get 336 ÷ 6 = 56 different groups of three people
from the eight people. This is a combination problem.
In the language of combinatorics, we say “eight choose
three is fifty-six.” We can calculate as follows:
8!
8 ⋅ 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅1
8 ⋅ 7 ⋅ 6
C
=
=
=
= 56
8
3
(
)
8 − 3
!⋅3!
5 ⋅ 4 ⋅ 3⋅ 2 ⋅1⋅ 3 ⋅ 2 ⋅1
3 ⋅ 2 ⋅1
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