Homework # 3 - Math 2236
The problems on this homework must be done alone. The honor code is in effect.
You may submit the solutions twice, if you wish.
First Name: Last Name:
1. In a deck of 52 cards, how many 5 card hands are 2 pair (that means 2 cards of one value, two of another value, and then a fifth card that is different than either of the pairs)?
a. 123,552
b. 247,104
c. 267,696
d. 292,032
e. 658,944
2. What is the probability of being dealt a 5 card hand of exactly 2 pair from a well shuffled deck of 52 cards?
a. 2.75\%
b. 4.75\%
c. 6.25\%
d. 9.50\%
e. 11.25\%
3. Which of these is congruent to 5+6 (mod 4)?
a. 0
b. 1
c. 2
d. 3
4. Which of these is congruent to 5\(\times\)6 (mod 4)?
5. Consider the 3 hat problem, but change the number of people to 2, where each is given a hat of 3 colors. In how many color combinations can the hats be distributed?
a. 1
b. 3
c. 6
d. 9
e. 12
6. In the variation given in question 5 with 3 hat colors and a team of 2 players, how many differnt color combinations can each player see when they look at their partner (don't over-think this one)?
7. Can the variation given in question 5 with 3 hat colors and a team of 2 players be won 100\% of the time with the appropriate strategy?
a. yes
b. no
8. If we change it to 2 hat colors and 2 players, can this variation be won 100\% of the time with the appropriate strategy? (You should understand that I'm asking you a question you already know the answer to.)