Algebra 2 help? Independent and Dependent Events?

Question

How many ways can six different books be arranged on a shelf if one of the books is a dictionary and it must be on an end? Could you please not only tell me the answer, but show me how you got it so i can work the rest of the problems? Thanks a bunch

Answer 1

5x4x3x2x1=120.

the reason.

lets say there are books A B C D E F. D is at the end (dictionary.)

(5 choices for 1st spot)(4 choices)(3)(2)(1)

after the 5 choices, lets say you put book A there, so thus the different possiblilities lessens. multiply the possibilities together to get the number of combinations.

Answer 2

Since dictionary must be put at the end,

we can only choose 5 books to put in the first,

after putting 1 book, we have only 4 book to choose from and so on..

Ways of arranging the book=5*4*3*2*1=120