Question

MEDAL FOR WHOEVER HELPS.
Sam, Pam, Ken and Jen are exchanging gifts for the holiday. Each name is written on a slip of paper and placed in a bowl. Sam is the first to randomly select a name from the bowl. How many different gift exchange pairings are there among Sam, Pam, Ken and Jen in which each person randomly selects a name other than their own name?

Answer 1

@Twitchie @adrynicoleb Please help me.

Answer 2

Well, Sam can pick from 3 people, Pam can pick from 3, Ken can pick from 2, Jen can pick from 1.

Answer 3

Thats what I thought wio. But the answer is 9.
btw this is a mathcounts question.

Answer 4

Well, \(3+3+2+1 =9\), though it is a bit strange.

Answer 5

wio, adrynicoleb, I have to go eat dinner at a restaurant. I'll be back in a long time so please keep answering but dont expect me to reply.

Answer 6

i'll probably be back at 6:30 maybe

Answer 7

wio, here is the explanation i got.

We can determine the answer by making an organized list. Suppose the friends select a name from the bowl in this order S, P, K and J. The table below shows the different pairings in which each person selects a name other than their own name:

There are 9 such gift exchange pairings.

Answer 8

table did not show up :( ill just draw it.

Answer 9

gtg now wio. ill give u a medal when i get back. thanks for helping.

Answer 10

but please keep trying to answer it.

Answer 11

Here's how it is done:

There are 4 factorial (4!) ways in which 4 people can choose 4 names
SAM PAM KEN JEN
To make things easier to track, we'll call Sam 1, Pam 2, Ken 3, and Jen 4
The attached graphic sows all 24 ways that 4 people can choose 4 names.
The ones marked off with a red arrow indicate the 9 ways in which none of the people choose their own names.

Answer 12

@wolf1728 come

Answer 13

hi wio and honorsstudent.

Answer 14

Someone please reply

Answer 15

Hello

Answer 16

hi wolf can i have a quick way to do it? (this is a mathcounts problem so i need to solve it quickly)

Answer 17

You mean the gift problem resulting in 9?

Answer 18

yea thats the problem

Answer 19

Why arent you guys replying?

Answer 20

Just taking a guess you could mention derangements - you need to have all the names NOT match their own names.

Answer 21

I have no idea David. Sorry. ._. Listen to the smart people :P

Answer 22

thanks for trying adrynicoleb. oh well

Answer 23

I can't get a formula - I'm just searching for what topic this might be

Answer 24

@adrynicoleb can u fan me i want to pm u

Answer 25

I'm guesing that the solution of 9 is found by determining the derangements of 4.
(A derangement is a sequence in which each member is out of order)
1234 is NOT a derangement
4312 IS

Answer 26

About math? @DavidUsa

Answer 27

From Wikipedia (can you use the link as a answer?) the derangements for
3 people 2
4 people 9
5 people 44
6 people 265
7 people 1854
8 people 14833
9 people 133496
From Wikipedia
http://en.wikipedia.org/wiki/Derangement

Answer 28

Yeah @adrynicoleb

Answer 29

i dont understand wolfe.

Answer 30

Well, I suck at math. So that wouldn't work out very well...

Answer 31

not a question

Answer 32

I have found a formula !!!
http://math.illinoisstate.edu/day/courses/old/305/contentderangements.html

Answer 33

wolf can u summarize it here? im in 6th grade thats gonna give me adhd

Answer 34

all that text

Answer 35

I am not good at anything related to math...

Answer 36

not a question i want to talk to u just pm u@adry

Answer 37

ok adry?

Answer 38

WOW they are asking this fro the 6th grade? Derangements???????

The total way the names can be drawn = number of people factorial
4! means factorial = 4*3*2*1 = 24
That's ALL the ways ALL the names are drawn
Now to figure the derangements.

Answer 39

no im advanced math dude. this is mathcounts not classwork. i got 5th individual for chapter.

Answer 40

Derangements for 4 people = 4! *[1 - (1/1!) + (1/2!) - (1/3!) + (1/4!)]
= 24 * (.5 -.33333333333 + 1/24)
= 24 * .375
= 9

Answer 41

Made a mistake - 1/3! = 1/6 which equals .1666666666666666
All that's needed is to change in my nswer is to change the .333333333333 to
.166666666666666

Answer 42

i dont understand but i probably wont anyway so u can just leave now.

Answer 43

@adrynicoleb can u fan me? i want to pm you.

Answer 44

Okay - I'm glad I found the formula - send a message if you want it explained some more.
Glad I could help you out.

Answer 45

ok bye wolf