math, help
posted by student .
How did they solved this problem i got this one wrong on my quizz.
Pizza Varieties A television commercial for Little Caesars
pizza announced that with the purchase of two pizzas, one could receive free any combination of up to five toppings
on each pizza. The commercial shows a young child waiting in line at Little Caesars who calculates that there are
1,048,576 possibilities for the toppings on the two pizzas.*
a. Verify the child’s calculation. Use the fact that Little Caesars has 11 toppings to choose from. Assume that the order of the two pizzas matters; that is, if the first pizza
has combination 1 and the second pizza has combination
2, that is different from combination 2 on the first pizza and combination 1 on the second.
The answer that's in the back of the book: 1, 048,574
b. In a letter to The Mathematics Teacher, Joseph F. Heiser
argued that the two combinations described in part a
should be counted as the same, so the child has actually
overcounted. Give the number of possibilities if the
order of the two pizzas doesn’t matter.
The answer they got was: 524,800
Consider first the number of ways a pizza can be prepared with 0, 1, 2, 3, 4 or 5 toppings selected from leven possible choices. That number is
11!/6!5! + 11!/7!4! + 11!/8!3! + 11!/9!2! + 11 + 1. The "1" represents no toppings at all.
That number is 462 + 330 + 165 + 55 + 11 = 1 = 1024. When two pizzas are made, the number of possible combinations for two (including duplicates) is (1024)62 = 1,048,576
Any differences from that number are probably the result of excluding duplicate pizzas.
That (1024)62 should have been (1024)^2. I didn't hit the shift key hard enough
thank you i got it earlier i wasn't seeing a step...
Respond to this Question
Similar Questions

Math
Julio ordered towo pizzas for dinner Friday. Dad ate 3/4 of one pizza, Jenny ate 1/8 of a pizza, Danny ate 1/4 of a pizza, and Mom ate 1/2 of a pizza. What fraction of a pizza was left for a midnight snack? 
Math
Julio ordered towo pizzas for dinner Friday. Dad ate 3/4 of one pizza, Jenny ate 1/8 of a pizza, Danny ate 1/4 of a pizza, and Mom ate 1/2 of a pizza. What fraction of a pizza was left for a midnight snack? 
Math
If you ordered two pizzas for dinner Friday. Date ate 3/4 of one pizza, Jenny ate 1/8 of a pizza, Danny ate 1/4 of a pizza, and Mom ate 1/2 of a pizza. What fraction of a pizza was left for a midnight snack? 
4th grade math
If you ordered two pizzas for dinner Friday. Dad ate 3/4 of one pizza, Jenny ate 1/8 of a pizza, Danny ate 1/4 of a pizza, and Mom ate 1/2 of a pizza. What fraction of a pizza was left for a midnight snack? 
Math
Hello, I have a probability problem on combination that is not easy to solve for me, and I need help. Thank you. Probleme: Problem: Little Caesar's Pizza had a commercial on tv that said you could buy 1 pizza and get another one free, … 
math
The pizza restuarant has a special off today: 3 pizzas for $25. The soccer team is ordering pizza, if each player eats 1/4 pizza, how many players will 3 pizzas serve? 
Math
When they dial 3 and turn the oven on, it is like pushing the old button 3 times. That means if they start with one pizza in the oven, dial 3, and turn the oven on, they will get 27 pizzas. (33 = 27) Then if they dial 3 and turn the … 
math
Mrs walkers ordered 10 pizza's for a party . Each pizza is cut into 8 slices the list below show the fraction of each pizza that was left after the party. 3/8,4/8,4/8,5/8,6/8,7/8,2/8,4/8,5/,3/8 1.Make a line plot of the fractions of … 
Elemements of Math
Little Caesar's Pizza had a commercial on television that claimed you could buy one pizza and get another one free, with up to 5 toppings per pizza (do not count the pizza sauce or the cheese as a topping). The dialogue on the commercial … 
Math
Cougar Pizza Parlor has just opened up across the street. You are thinking of inviting some friends over for pizza and ordering from Cougar's. You want to get the most pizza for the money. The menu shows the following prices. 6 inch …