Asa, Bill, Cathy, Dino, and Eve are randomly seated in a row of 5 seats. Find the probability that Asa will sit next to Bill.

- anonymous

- jamiebookeater

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- anonymous

View asa and bill as one person. Then, find the number of ways the four "people" can fill the seats. Then view bill and asa as one person, and do it again. Sum the two. Thats the total number of ways bill and asa can sit next to each other.
Now, find the total number of ways the five students can sit in the row. The probability they sit next to each other is the the number of ways they can sit next to each other divided by the number of ways they can sit overall.

- anonymous

Note that order is important!

- anonymous

can u show the work?? lol

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## More answers

- anonymous

Can you?

- anonymous

9 / 5!

- anonymous

8 / 5!

- anonymous

what?
It's supposed to be a fraction

- anonymous

you have ABCDE , there are 5! ways of sitting them. that will be your denominator

- anonymous

the favorable is AB sitting together, you can have oh...

- anonymous

you can have AB, BA , and there are 4 places , so 4* 2

- anonymous

thats your numerator

- anonymous

what's the numerator?

- anonymous

8

- anonymous

so you have 8/120

- anonymous

that's not a choice though
(1) 1/60 (2) 2/5 (3) 1/10 (4) 4/15

- anonymous

oh

- anonymous

ok there are 2x4x3! in the numerator

- anonymous

so 2/5

- anonymous

wait 24/120 is 1/5
not 2/5

- anonymous

no thats 48/120

- anonymous

oh, I got u

- anonymous

2x4x3! = 2x4x(3x2x1)

- anonymous

give me medal NOW

- anonymous

I got 2/5.

- anonymous

me too

- anonymous

there are 2 ways for AB to sit next to each other, they can move around in 4 different places, then there are 3! for the rest of the other people to sit

- anonymous

wait so basically
it's 5!/ 2!4! ???

- anonymous

shut up omg. Look at the method i proposed. 2(4!)/(5!)

- anonymous

well you treat AB as K, so you have K C D E , and how many ways can you reararnge that

- anonymous

then K has 2! ways

- anonymous

shut up, omg, GROW UP

- anonymous

u 2 r arguing?

- anonymous

so you have K C D E , where K is AB, and you have 4! ways of rearranging that, but K is actually AB or BA, so 4! * 2!

- anonymous

azn, can you give me medal, i got answer first

- anonymous

can u guys explain what u did?

- anonymous

i did

- anonymous

explain then
right now

- anonymous

treat AB as K, since they always sit next to each other, so you have K C D E , correct ?

- anonymous

yea

- anonymous

so how many ways to rearrange K C D E ?

- anonymous

24

- anonymous

right, but for each one of those arrangements, you have AB or BA

- anonymous

since they can swap

- anonymous

so you need 24 x 2

- anonymous

in other words, K can be AB or K can be BA

- anonymous

so you have 24 with AB , and 24 with BA, so 24 + 24

- anonymous

ok and how did u get the 5! part

- anonymous

thats the number of ways to rearrange A B C D E

- anonymous

5 !

- anonymous

wheres my medal

- anonymous

PLEASSSSSSSSEEEEEEEEEEEEEEEEEEEEEEEEE

- anonymous

oh I got it

- anonymous

how do I give u a medal? It's my first time here, how?

- anonymous

next to my name

- anonymous

it should say give medal

- anonymous

it doesn't

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