You have 3 hard cover books and 5 soft cover books. How many different ways can you arrange these books on a shelf if the three hard cover books have to be next to each other?

Question

You have 3 hard cover books and 5 soft cover books.  How many different ways can you arrange these books on a shelf if the three hard cover books have to be next to each other?

campbell_st · Answer

ok... so treat the 3 hard cover books as 1 unit

then there are 6 items to place on the shelf 

this can be done 6! ways

and the 3 hardcover books can be arranged in 3! ways

to the total number of arrangements is 

6! x 3! 

hope this makes sense.