Problem 0. How many
committees of 3 women can be made from 20? How many committees
of 3 men and 3 women can be made from 10 men and 20 women?
Problem 1. A bridge hand consists of any 13 cards
selected from a 52-card deck without regard to order.
a. How many bridge hands are there?
b. How many bridge hands have only red cards?
c. How many bridge hands have all 4 aces?
d. How many bridge hands have 5 spades, 4 hearts, 3
diamonds and 1 club.
Problem 2. You are making a pizza. There
are 3 types of dough: white, wheat, and white whole
grain. There are 4 types of cheese available, and 10 different
toppings. (Cheese isn't considered a topping for this
problem.) How many types of pizza can be made if:
a.
You
pick one type of dough, 2 different types of cheese, and 4 toppings?
b.
You
pick one type of dough, any combination of the 4 cheeses, and any
combination of toppings? (Warning: "Any combination" is
English and not necessarily the math definition. What it
means is that you could have no cheese, any combination of 2
cheeses, all 4, etc.)
c.
You pick one type of dough, any combination of the 4
cheeses as long as there is one cheese, and any combination of 1, 2
or 3 toppings?
Problem 3. How many 7 letter words can be made
(mathematically, a word is just a group of letters and
doesn't even have to be pronounceable) from the letters PAINFUL if
a.
we
can repeat the letters?
b.
no
repeated are allowed?
c.
What
if the word is 4 letters long and we can repeat the letters?
d.
What
if the word is 4 letters long and we can not repeat the
letters?
Problem 4. How many 13 letter words can be made from
the letters in GOOD DEED DOTTY if
a.
we
can repeat the letters as many times as we want?
b.
we must rearrange the letters?
Problem 5. A poke hand
consists of any 5 cards selected from a 52-card deck without regard
to order.
a. How many poker hands are there?
b. How many poker hands have only red cards?
c. How many poker hands have all 4 aces?
d. How many poker hands are considered a
four-of-a-kind?
e. How many poker hands are considered a
three-of-a-kind?
f. How many poker hands are considered a pair of
queens?
g. How many poker hands are considered one pair?