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Counting Problems:
1.
A party has 50 persons. 45 of them are boys. 5 are girls. If we select randomly 6 people,
a.) What is the probability to have exactly 1 girl?
Pr[Select exactly 1 girl] =
(
29
(
29
(
29
45
5
5
1
50
6
0.384
=
b.) To have at least 2 girls?
Pr[Select at least 2 girls] = 1 – Pr[Select no girls] – Pr[Select exactly 1 girl]
(
29
(
29
(
29
(
29
(
29
(
29
45
5
45
5
6
0
5
1
50
50
6
6
1
0.103
= 

=
2.
There are 20 people at a party.
a.) If there are 10 men and 10 women, how many pairs (men with women) are there?
# of pairs = 10!
2245
3.63 x 10
6
(Line up women and assign men)
b.) If all 20 are men (or women) how many pairs are there?
# of pairs =
(
29
(
29
(
29
(
29
20
18
4
2
10
2
2
2
2
20!
2
10!
10!
=
L
2245
6.55 x 10
8
c.) If there are 10 men and 10 women, but we pair women with women and men with men,
how many pairs are there?
# of pairs =
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
2
10
8
4
2
10
8
4
2
5
2
2
2
2
2
2
2
2
10!
2
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 Fall '08
 Stedinger

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