How many permutations of 1 1 2 2 3 3 4 4 5 5 are there in wh

How many permutations of 1, 1, 2, 2, 3, 3, 4, 4, 5, 5 are there in which no two adjacent numbers are equal?

Solution

We know that the number of permutations of 1,1,2,2,3,3,4,4,---,n,n with no two adjacent

terms are equal is =[(2n)!]/2^n

                 In our problem n=5

                                 =[(2*5)!]/2^5

                                 =[10!]/2^5

                                 =[10*9*8*7*6*5*4*3*2*1]/[2*2*2*2*2]

by doing cancllation we get

                                  =10*9*4*7*3*5*2*3

                                  =226800