Question 12

In the galaxy “Andromeda”, a planet named “Exo” has a city called “Azith”. The city has analphabet system that consists of 48 letters and an octo-decimal number system (base -18). Theregistration number on the number plate of a vehicle in the city has two parts. The first part is the alphabetpart that consists of three letters and the second part is the number part that consists of 3 digits. The cityadministration issues all kinds of registration numbers with following restrictions:
a. The letters in the alphabet part are in ascending order and all letters must be distinct.
b. In the number part, the first digit is three more than the third digit.
Find the number of possible registration numbers available in the Azith city.

Solution

There are 48 alphabets out of which we need 3

So, no. of ways of selecting 3 alphabets from 48 alphabets is $$^{48}C_3$$

Since we need to arrange these alphabets in ascending order so there is only one possible way for every three alphabets.

The first digit is 3 more than the third digit.

For a particular first digit there will be a particular third digit but the 2nd digit can be any of the numbers

So, no. of ways of selecting first digit= 15

No. of ways of selecting 2nd digit = 18

Therefore, total no. of ways = $$^{48}C_3\times\ 15\times\ 18$$ = 4669920

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