How many ways can we arrange letters a b c d so that b does

How many ways can we arrange letters a, b, c, d so that b does not immediately follow a and c always follows b.

Solution

Here we need those arrangements which contain \'bc\' but not \'ab\' .

We consider \'bc\' as a single alphabet and hence we get 3 alphabets \'a\' , \'bc\' and \'d\' to arrange.

We can arrange these 3 alphabets among themselves in 3! = 6 ways.

Out of these 6 arrangements the arrangement \'a\',\'bc\',\'d\' is not conformable.

Hence only 6-1 =5 such arrangements are possible.