Tim has an encyclopedia in 5 volumes: a–c, d–f, g–j, k–n, and o–z. other than alphabetically (ascending or descending), how many ways can these volumes be arranged?

a) 120
b) 118
c)25
d)insufficient data

is it a? !

Option: B is the correct answer.

            B) 118

We know that the arrangement of n item is given by :

                    n!

Here we have a total of 5 volumes that need to be arranged.

i.e. n=5

Hence, the number of ways of arranging these 5 volumes are:

              5!=5×4×3×2×1=120

Also, we have to exclude the case such that the ascending or descending order of arrangements are discarded.

i.e. we have to exclude two cases hence the remaining cases are:

                   120-2=118

( Since there is only one way of arranging all of them in increasing order and only one way of arranging all of them in decreasing order )

Hence, the number of ways these volume can be arranged are:

                                  118

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