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Counting:

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  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 N+M ways to choose from group one OR group two. Or

  2. Joe’s 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 Sandwich 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? 26·26·26·26·26=11,881,376 How many passwords of eight lower-case letters? 26·26·26·26·26 ·26·26·26 =208,827,064,576 How many passwords of eight characters that are upper or lower case letters,0-9,~,!,@,#,$,%,^,*,-,_,=,+,{,},[,],:,;,comma,period,?,\,/? 85·85·85·85·85 ·85·85·85 =2,724,905,250,390,625 (two quadrillion seven-hundred-twenty-four trillion . . .)

  6. The Incredibly PopularBarb the BratDoll • 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: (2+1)•(2+5•(3+1))•3 = 198

  7. Joe’s 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”. Joe’s Regular – 1 topping Joe’s Deluxe – 1 meat, 1 other