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# For people in the future

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in how many different ways can 4 students stand in a straight line if two of the students refused to stand next to each other?

Aug 18, 2020

#1
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There are 3 ways to stand so they do not have to stand next to each other

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0101             the other two slots have 2 ways to be arranged     3 x 2 = 6 ways

Guest answer is correct..... I neglected the fact that you could switch the two students around for a total of SIX ways they would not have to stand next to each other.....then the other two slots have two ways     soooo     6 x 2 = 12  ways

Thanx, Guest !

Aug 18, 2020
edited by ElectricPavlov  Aug 18, 2020
#2
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Give students names or initials:
A=Alice, B=Bob, C=Cathy, D=David
Suppose Alice and David do not want to stand next to each other, then you have the following arrangements: 4! / 2! = 12. A,D cannot stand next to each other
{A, B, C, D} | {A, B, D, C} | {A, C, B, D} | {A, C, D, B}  {B, A, C, D} | {B, D, C, A} | {C, A, B, D} | {C, D, B, A}  {D, B, A, C} | {D, B, C, A} | {D, C, A, B} | {D, C, B, A}

Aug 18, 2020