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

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

total permutations of 26 alphabet will be26*25*24=15600.

out of these permutations, for ex. consider 2 letter permutations out of three letters.. AAB,AAC etc..

in these if we interchange the 1st two letters,, the identity wil not change.. so.. these pairs will be substracted from the total..

those will be 26*3*26=2028

In addtion,consider 3 letters. The order of AAA,BBB etc interchanging will not differ. so remove this 26*7=182 permutations and keep one set of these..

So, the total permutations will be 15600-2028-182=13390 different exchanges can be indicated.

please do reply whether my ans. was correct or not.