Counting:

1
Counting
If group one has N choices, and group two
has M choices, then there are N?M ways
to choose from group one AND then from
group two.
And

If group one has N choices, and group two
has M choices, then there are NM ways
to choose from group one OR group two.
Or
2
Joes Lunchbox

• Cheese
• Turkey
• Ham
• Roast Beef

Sandwiches
Soups

• Matzo Ball
• Lentil
• Tomato

How many choices do you have for
soup ___ a sandwich?
3
Answer 7

• Cheese Sandwich
• Roast Beef Sandwich
• Turkey Sandwich
• Ham Sandwich
• Matzo Ball Soup
• Lentil Soup
• Tomato Soup

4
Answer 12
Matzo Ball Soup
Cheese Sandwich Roast Beef Sandwich Turkey S
andwich
Ham Sandwich
Lentil Soup
Tomato Soup
Matzo Ball Soup
Lentil Soup
Tomato Soup
Matzo Ball Soup
Lentil Soup
Tomato Soup
Matzo Ball Soup
Lentil Soup
Tomato Soup
5
Strong Passwords

• At least eight characters.
• At least one number and one letter.
• No spaces,,,, ,(,),,

How many passwords of five lower-case letters?
262626262611,881,376
How many passwords of eight lower-case letters?
2626262626 262626 208,827,064,576
How many passwords of eight characters that are
upper or lower case letters,0-9,,!,_at_,,,,,,-
,_,,,,,,,,,comma,period,?,\,/?
8585858585 858585 2,724,905,250,390,625
(two quadrillion seven-hundred-twenty-four
trillion . . .)
6
The Incredibly Popular Barb the Brat Doll

• Comes with
• Two Hats
• Two Dresses
• Three Skirts
• One Pair Slacks
• Five Blouses
• Three Pairs Shoes

How many outfits (grocery store acceptable)
can we make for Barb?
Answer (21)(25(31))3 198
7
Joes Pizza Place

• Crusts
• Thin
• Regular
• Deep Dish
• Stuffed Crust

• Sauces
• Regular
• Spicy

• Meats
• Pepperoni
• Sausage
• Canadian Bacon
• Ham

• Other Toppings
• Extra Cheese
• Mushrooms
• Green Peppers

All Come in 10,12 or 16. Joes Regular 1 top
ping
Joes Deluxe 1 meat, 1 other