We are given
total number of dolls =5
and there are five spaces only to be arranged in
In first space:
Any five dolls can be put in
so, number of ways of putting dolls in first space is 5
In Second space:
One doll is already put in first space
so, only four dolls can be put in
so, number of ways of putting dolls in second space is 4
In Third space:
One doll is already put in second space
so, only three dolls can be put in
so, number of ways of putting dolls in third space is 3
In Fourth space:
One doll is already put in third space
so, only two dolls can be put in
so, number of ways of putting dolls in fourth space is 2
In Fifth space:
One doll is already put in fourth space
so, only one dolls can be put in
so, number of ways of putting dolls in fifth space is 1
so, total number of ways five dolls can be arranged
[tex] =5*4*3*2*1 [/tex]
[tex] =120 [/tex].................Answer
