Category 4 Arithmetic Meet #5 Worksheet With Answers - 2001 Page 12
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12Solutions to Category 4
Arithmetic
Meet #5, March 2006
1. For each of the 5 different bicycles Thornton could
Answers
buy, there are 4 helmet, and 2 noise makers. We use the
multiplication principle to calculate that there are
1. 40
5 × 4 × 2 = 40 different possible set-ups.
2. 70
2. This is a “combination” problem, rather than a
11
3.
“permutation” problem, since the order in which the four
36
people are chosen does not matter. If it were a
permutation problem, we would simply multiply as
follows 8 × 7 × 6 × 5 = 1680 . But the same four people
could be chosen in any of 4 × 3 × 2 ×1 = 24 different
ways, so we must divide 1680 by 24 to get 70 different
groups of 4 people. Using the general formula for
combinations, we calculate as follows:
8!
8!
8 × 7 × 6 × 5
C
=
=
=
= 7 × 2 × 5 = 70 .
12
4
(
)
8 − 4
!⋅4!
4!⋅4!
4 × 3 × 2 ×1
3. The 36 possible sums are shown in the table below
with the 11 prime numbers in bold. The probability of
11
rolling a prime sum is
.
36
+
2
4
8
16 32 64
1
3
5
9
17 33 65
2
4
6
10 18 34 66
3
5
7
11 19 35 67
4
6
8
12 20 36 68
5
9
13 21 37 69
7
6
8
10 14 22 38 70
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