Posted by navroz on Tuesday, January 3, 2012 at 2:12pm.
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 - Steve, Tuesday, January 3, 2012 at 2:31pm
4+5+6+7 = 22
So, there would be
- math - navroz, Tuesday, January 3, 2012 at 2:43pm
but why is the denominator 4!5!6!
- math - Steve, Tuesday, January 3, 2012 at 2:53pm
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 - navroz, Tuesday, January 3, 2012 at 3:11pm
but wat happened to the 7 shouldnt it be 4!5!6!7!
- math - Steve, Tuesday, January 3, 2012 at 3:12pm
There are 7 assorted other cookies. Thus, they are different, and can be eaten in distinguishable orders.
Answer this Question
More Related Questions
- math - the cookie monster has a package of cookies with him consisting of 4 ...
- Math - A cookie jar contains 3 chocolate-chip, 2 peanut butter, 1 lemon, 1 ...
- finite math - A tray contains 14 chocolate chip cookies and 16 oatmeal raisin ...
- math - A tray contains 11 chocolate chip cookies and 15 oatmeal raisin cookies. ...
- math - One night Ms. Factor baked chocolate chip cookies. She used a 20-ounce ...
- math - Mary is baking cookies for her school bake sale. For every 5 chocolate ...
- Statics - In a chocolate chip cookie investigation, you decide to compare two ...
- Probability - In a cookie jar, there are 6 choco chip cookies and 8 oatmeal ...
- Math - It is a story problem. Courtney has 27 chocolate chip cookies and 36 ...
- Math - There are 4 chocolate chip cookies and 12 oatmeal cookies in a jar. If ...