# math

posted by .

the cookie monster has a package of cookies with him consisting of 4 chocolate chip, 5 raisin and 6 almond nut, 7 other different assorted cookies. if he reaches into the package and eats all the cookies, eating one cookie at a time, how many different eating orders are there?

• math -

4+5+6+7 = 22

So, there would be

22!
-------
4!5!6!

= 542,052,820,108,800

• math -

but why is the denominator 4!5!6!

• math -

If all the cookies were different, you'd have just 22! different ways. But, if you just consider the 4 chocolate chip cookies, they are indistinguishable from each other. If they were different, then there would be 4! different ways to eat the chocolate chip cookies. But you don't care which of them you are eating, so you divide by the 4! ways which are the same.

Consider the case of 4 cookies, 3 of which are A, and also a single B. If you write down all the ways to eat them, numbering the A's, you get

A1 A2 A3 B
A1 A2 B A3
A1 A3 A2 B
A1 A3 B A2
A1 B A2 A3
A1 B A3 A2

A2 A1 A3 B
A2 A1 B A3
A2 A3 A1 B
A2 A3 B A1
A2 B A1 A3
A2 B A3 A1

A3 A1 A2 B
A3 A1 B A2
A3 A2 A1 B
A3 A2 B A1
A3 B A1 A2
A3 B A2 A1

B A1 A2 A3
B A1 A3 A2
B A2 A1 A3
B A2 A3 A1
B A3 A1 A2
B A3 A2 A1

As you can see, there are 4! = 24 ways to eat the cookies. But, if all the A1 A2 A3 are replaced by just A, we have only

A A A B
A A B A
A B A A
B A A A

which is 4!/3! = 4

Expand that to your problem, and you see why we divide by n! if there are n identical objects.

• math -

but wat happened to the 7 shouldnt it be 4!5!6!7!

• math -

There are 7 assorted other cookies. Thus, they are different, and can be eaten in distinguishable orders.

## Similar Questions

2. ### math

the cookie monster has a package of cookies with him consisting of 4 chocolate chip, 5 raisin and 6 almond nut, 7 other different assorted cookies. if he reaches into the package and eats all the cookies, eating one cookie at a time, …
3. ### Statics

In a chocolate chip cookie investigation, you decide to compare two cookie sources. Source 1: Mom mails to you a package containing a dozen of her homemade chocolate chip cookies. Source 2: You purchase a dozen of a store brand of …
4. ### finite math

A tray contains 14 chocolate chip cookies and 16 oatmeal raisin cookies. How many ways can a child select 4 cookies that include at least 1 chocolate chip cookie?
5. ### math

A tray contains 11 chocolate chip cookies and 15 oatmeal raisin cookies. How many ways can a child select 4 cookies that include at least 1 chocolate chip cookie?
6. ### math

Mary is baking cookies for her school bake sale. For every 5 chocolate chip cookies she makes 2 oatmeal raisin cookies. If she keeps this ratio, and bakes 84 cookies total, what will be the ratio of chocolate chip cookies to oatmeal …
7. ### math

One night Ms. Factor baked chocolate chip cookies. She used a 20-ounce package of cookie dough to make 3 dozen cookies. What was the average weight of each cookie.
8. ### Algebra

If you make a bunch of cookies, and ten of your friends wanted some cookies. There are, in total, 5 dozen (60) cookies. Each dozen is a different kind; chocolate chip, oatmeal, no-bake, peanutbutter, and gingerbread. If you put all …
9. ### Chem (HELP!!)

Test tomorrow too! I don't understand how to do these at all! HELP PLEASE _______________________________ 3.) 11.45 L of milk spilled on the floor. How many gallons spilled?
10. ### Math

I don't know how to make an equation for this?

More Similar Questions