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?

underatedperson Aug 18, 2020

#1**+1 **

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

1001

1010

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 !

ElectricPavlov Aug 18, 2020

#2**+1 **

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}

Guest Aug 18, 2020