A family has 5 children. Two of the children are twin boys named Nick and James. The boys always sit next to each other, with Nick on the left side of James. In how many different orders could the children sit in a row of 5 chairs if the twins always sit next to each other?

Question

amorfide · Answer

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you have 5 over all
possible positions are 5!
but then you have 2 people together at all times so you count them as 2! as they can be arranged in two ways AB or BA
then you have 3! 
5!/3!2! 

someone correct me if i am wrong please as statistics is my worst part of math

anonymous · Answer

no but i have these answers as multiple choice
A. 24
B. 48
C. 60
D. 120

amorfide · Answer

oh my bad uhm...

amorfide · Answer

you have 5 people
2 of them are always together
count these 2 people as 1 person
so you have 4!
but these two people can be arranged AB or BA so multiply your answer by 2!

anonymous · Answer

@amorfide , the following statement made by you is wrong 
"but these two people can be arranged AB or BA"

Tip: Read the question again :)

anonymous · Answer

can you please help me?

amorfide · Answer

lol sorry :(

anonymous · Answer

@shivam_bhalla

amorfide · Answer

4! is right then?

anonymous · Answer

its not right its not one of the asnwers in the multiple choice

amorfide · Answer

4!=24
not sure if it is right though :S best answer i can give

anonymous · Answer

@@erica123 ,  4! = 24

anonymous · Answer

can you explain it to me please

anonymous · Answer

Let @amorfide do it for you :)

amorfide · Answer

you have 5 children
you have two children ALWAYS next to each otehr so think of these as 1 person so you subtract 1 from 5
4 people
you do 4! so you get 24
the question states these two only sit in one order  (Nick on the left side of James.)
so you multiply your answer by 1!
this gives you 24x1=24


if the question never stated that nick was on the left side of james
you would have had two possible ways for those to sit next to each other so you would have had 2! ways they can be arranged
then you would have had 4! x 2!

anonymous · Answer

I hope @erica123  that was clear to you :)

anonymous · Answer

i still dont get it

anonymous · Answer

where did you get 24 from

amorfide · Answer

4! = 4 x 3 x 2 x 1

anonymous · Answer

but theres 5 chairs?  i dont know im so confused :(

anonymous · Answer

Basically n! = n x (n-1) x (n-2) x (n-3) x........

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