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? 22!

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why is the denominator 4!5!6!????

I was about to go into an explanation, when I noticed that Steve had answered this exact question already in your previous post.

Please do not post the same question again without checking if your previous post of that question has been answered. This way we can avoid unnecessary duplication on the part of the tutors.

The denominator in the equation represents the total number of ways to arrange the cookies of each type within their respective groups. In this case, we have 4 chocolate chip cookies, 5 raisin cookies, and 6 almond nut cookies. To understand why the denominator is calculated as 4!5!6!, let's break it down:

- 4!: This represents the number of ways to arrange the 4 chocolate chip cookies. The factorial symbol (!) indicates that we want to multiply a series of descending numbers. In this case, it means 4 * 3 * 2 * 1, which equals 24.
- 5!: Similarly, this represents the number of ways to arrange the 5 raisin cookies. So, 5! = 5 * 4 * 3 * 2 * 1 = 120.
- 6!: Finally, this represents the number of ways to arrange the 6 almond nut cookies. Therefore, 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720.

To find the total number of different eating orders, we multiply these three factorials together: 4! * 5! * 6! = 24 * 120 * 720 = 12,441,600.

Therefore, there are 12,441,600 different eating orders for the cookie monster.