Problema Solution

Six children stand in a line outside their classroom. When they enter the classroom, they sit in a circle in random order. There are relatively prime positive integers m and n so that m/n is the probability that no two children who stood next to each other in the line end up sitting next to each other in the circle. Find m+n.

Answer provided by our tutors

Six children stand in a line outside their classroom. When they enter the classroom, they sit in a circle in random order. There are relatively prime positive integers m and n so that m/n is the probability that no two children who stood next to each other in the line end up sitting next to each other in the circle. Find m+n.

 

Solution:

m/n = 3!*3!/6! = 36/720 = 1/20

So m=1, n=20

m+n = 21