SOLUTION: An eight-volume set of reference books is kept on a shelf. The books are used frequently and put back in random order. a. How many ways can the eight books be arranged on the she

Question 1124667: An eight-volume set of reference books is kept on a shelf. The books are used frequently and put back
in random order.
a. How many ways can the eight books be arranged on the shelf ?
b. How many ways can the books be arranged so that Volume 5 will be the rightmost book?
c. Use the answers from (a) and (b) to find the probability that Volume 5 will be the rightmost
book if the books are arranged at random.
d. Explain how to compute the probability in (c) using another method.
e. If the books are arranged randomly, what is the probability that the last book on the right is
an even-numbered volume? Explain how you determined this probability.
f. How many ways can the books be arranged so that they are in the correct order, with volume
numbers increasing from left to right?
g. How many ways can the books be arranged so that they are out of order?
h. What is the probability that the books happen to be in the correct order?
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.
An eight-volume set of reference books is kept on a shelf. The books are used frequently and put back
in random order.

a.  How many ways can the eight books be arranged on the shelf ?

    8! = 8*7*6*5*4*3*2*1.


b.  How many ways can the books be arranged so that Volume 5 will be the rightmost book?

    7! = 7*6*5*4*3*2*1.


c.  Use the answers from (a) and (b) to find the probability that Volume 5 will be the rightmost
book if the books are arranged at random.

    P =  = .


d.  Explain how to compute the probability in (c) using another method.


e.  If the books are arranged randomly, what is the probability that the last book on the right is
an even-numbered volume? Explain how you determined this probability.

     =  = .


f.  How many ways can the books be arranged so that they are in the correct order, with volume
numbers increasing from left to right?

    1 way.


g.  How many ways can the books be arranged so that they are out of order?

    8! - 1.


h.  What is the probability that the books happen to be in the correct order? 

    .

Too many questions for one post.

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