Math

[fgbg]

In a certain country, television stations names contain either three or four letters and must start with either the letters R, T or Y. How many station names are available if the names end with C?

[aneesh.kg]

For three letter codes, draw three dashes.
One the last dash, we have just one possibility (which is C).
One the middle dash, we have 26 possibilities (any of the 26 alphabets).
One the first dash, we have 3 possibilities (R,T or Y).
So, Total number of 3-letter codes = 1 X 26 X 3

For four letter codes, draw four dashes.
One the last dash, we have just one possibility (which is C).
One the middle two dashes, we have 26 possibilities each (any of the 26 alphabets).
One the first dash, we have 3 possibilities (R,T or Y).
So, Total number of 4-letter codes = 1 X 26 X 26 X 3

So, Total number of codes = 1 X 26 X 3 + 1 X 26 X 26 X 3
= 26 X 3 X (1 + 26) = 26 X 3 X 27 = 2106 (Answer)