Permutation

For each of the problems below, (1) figure out whether this involves permutation with or without replacement, then (2) compute the solution. The first one has been done for you.

Word problem Replacement? Solution

	Word problem	Replacement?	Solution
1	Joy has picked out seven outfits for the week. She intends to wear each of them once, but she hasn’t chosen an order yet. How many different ways could she dress up this week?	Yes No	$\displaystyle permute\mbox{-}no\mbox{-}replace(7, 7)$ $\displaystyle = \frac{7!}{(7-7)!}$ $\displaystyle = \frac{7!}{(0)!} = \frac{5040}{1} = 5040$
2	Mrs. Burke’s cell phone has a 6-character password. Her son is trying to unlock it to play a game. How many possible passwords does he have to guess?	Yes No
3	The dentist has 8 different stickers to give away to the next patients `A` through `H`. How many different ways could she give them out?	Yes No
4	Eric Allatta is the head chef at the top restaurant in Santa Fe. His speciality is four-color enchilada platter, with each enchilada covered in a different sauce. How many ways can he order them on the plate?	Yes No
5	A magician opens a fresh deck of 52 cards, and asks an audience member to pick six of them. He says he’ll guess all six - in order. What are the chances he’ll guess them correctly?	Yes No
6	Emma is knitting a hat, and each row of stitching can be a different color. She has three different colors of yarn to choose from, and the hat has 30 rows. How many different designs could she make?	Yes No

Joy has picked out seven outfits for the week. She intends to wear each of them once, but she hasn’t chosen an order yet. How many different ways could she dress up this week?

Yes No

$\displaystyle permute\mbox{-}no\mbox{-}replace(7, 7)$ $\displaystyle = \frac{7!}{(7-7)!}$ $\displaystyle = \frac{7!}{(0)!} = \frac{5040}{1} = 5040$

Mrs. Burke’s cell phone has a 6-character password. Her son is trying to unlock it to play a game. How many possible passwords does he have to guess?

Yes No

The dentist has 8 different stickers to give away to the next patients A through H. How many different ways could she give them out?

Yes No

Eric Allatta is the head chef at the top restaurant in Santa Fe. His speciality is four-color enchilada platter, with each enchilada covered in a different sauce. How many ways can he order them on the plate?

Yes No

A magician opens a fresh deck of 52 cards, and asks an audience member to pick six of them. He says he’ll guess all six - in order. What are the chances he’ll guess them correctly?

Yes No

Emma is knitting a hat, and each row of stitching can be a different color. She has three different colors of yarn to choose from, and the hat has 30 rows. How many different designs could she make?

Yes No

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