How many different fivesentence paragraphs can be formed if

How many different five-sentence paragraphs can be formed if the paragraph begins with \"He thought he saw a shape in the bushes\" followed by \"Mark had told him about the foxes\"? A television programmer is arranging the order that five movies will be seen between the hours of 6 P.M. and 4 A.M. Two of the movies have a G rating, and they are to be shown in the first two time blocks. One of the movies is rated NC-17, and it is to be shown in the last of the time blocks, from 2 A.M. until 4 A.M. Given these restrictions, in how many ways can the five movies be arranged during the indicated time blocks?

Solution

Ans(11):

There are total 5 time slots for movies.

there are 2 G rating movies and to be shown in first two time blocks so these two movies can be arranged in 2 ways in first two time blocks.

NC-17 rated movies is to be shown in last time block so that can be done in 1 way

now 2 movies are left and 2 times blocks are left

so 2 movies can be arranged in the remaining time blocks in 2 ways

hence total number of ways for the 5 movies are = 2*2*1=4

Hence final answer is 4 ways