So I have 4 Math books, 1 Economic book and 1 Physics book. I want to arrange them on a straight line. What is the probability of the book arrangement so that there is no 3 or more Math books adjacent to each other? So MMEMMP is allowed but MMMEMP is not allowed.
The answer is 0.4.
Total number of ways of arranging books= $6!/4!$=$30$ Now take all four math books as one object and permute in possible ways . It will be $3!$=$6$ Now take three Math book as one object and the other Math book should not be placed on either side of the three Math books. Therefore number of ways of arrangement = $2*3!$. These cases need to be subtracted from the sample space . You would be getting your answer as $12$. Probability would be $12/30$ which is $0.4$.