Name of the Exchange

In Great Britain some years back the first three letters of a telephone number used to indicate the name of the exchange. How many such arrangements of 3 letters is it possible to devise form the 26 letters of the alphabet?

Answer:  

 26 x 25 x4 = 15600. – This is an example of ‘Permutation of 26 different letters taken 3 at a time’. It is written in mathematical language as 26 p³

It is easy to arrive at this calculation really, when expressed in terms of factorials. It is result of dividing factorial 26 by factorial (26-3).

Generally speaking the number of permutations of n things if only r are taken at any one time is or factorial n divided by factorial (n-r) n p ͬ