HOMEWORK 1 SOLUTIONS
EE250 Spring 2009
SJSU  Electrical Engineering
Problem 1
[10 points]
a) A person draws 6 cards from a deck of 52 cards. What is the probability that he has a royal
Fush? To obtain a royal Fush, he must have ace, king, queen, jack, and ten of the same suit.
Solution:
There are 4 possible royal Fushes using 5 cards. The 6th card can be any card
(525 =47 possibilities). Hence,
P
(
Royal Flush
) =
4
×
47
C
52
6
.
b) A house has 12 rooms (10 bedroom and 2 living rooms). We want to paint 4 yellow, 5 red
and 3 purple. We do not want the living rooms to be the same color. In how many ways this
can be done?
Solution:
You can choose 4 rooms you want to paint yellow; then, choose 5 rooms you want
to paint red; the rest of them will be painted purple.
N
=
C
12
4
C
8
5
.
The number
N
includes the cases where the living rooms have the same color. Let’s count
these: Let
N
Y
,N
R
,N
P
denote the number of ways that the rooms can be painted when both
of the living rooms are painted yellow, red, and purple respectively.
N
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 Spring '09
 Sirkeci
 Electrical Engineering, Probability theory, possible values, green die, blue die

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