Category 4 Arithmetic Meet #5 Worksheet With Answers - 2001 Page 10
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12Solutions to Category 4
Arithmetic
Meet #5, March/April 2005
Average number of correct answers: 1.05 out of 3
1. The situation calls for the combination 8 choose 5,
Answers
which can be calculated as follows:
1. 56
8!
8 ⋅ 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅1
C
=
=
= 56
8
5
1
(
)
8 − 5
!⋅5!
3 ⋅ 2 ⋅1⋅ 5 ⋅ 4 ⋅ 3⋅ 2 ⋅1
2.
5
3. 11,793,600
2. The prime numbers on the number cube are 2, 3, and
5, which is 3 out of 6 numbers. The prime numbers on
the spinner are 2, 3, 5, and 7, which is 4 out of 10
numbers. The probability that he gets a prime number on
both the number cube and the spinner is the product of
the individual probabilities. Thus, we get
3
4
1
2
1
.
⋅
=
⋅
=
6
10
2
5
5
3. First of all, we have to look at the proper factors of
28. They are 14, 7, 4, 2, and 1. It turns out that the sum
of the proper factors of 28 is 28, which is why it is called
a perfect number. This means that Señor Generosa will
give out all $28 to five lucky students. It does make a
difference if a particular student gets $14 or $1, so this is
a permutation, not a combination. So the money can be
given out in the following number of ways:
28!
28!
= 28 ⋅ 27 ⋅ 26 ⋅ 25 ⋅ 24 = 11,793,600 .
P
=
=
28
5
(
)
28 − 5
!
23!
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education