Question

In a city, the bus route numbers consist of natural numbers less than 100 followed by one of the letters A, B, C, D, E, and F. How many different bus routes are possible?
A) 486
B) 480
C) 594
D) 524

Answer 1

Hint:
First of all, we’ll look into the exact number of buses then we’ll see how many specific cases can be made by combining the bus number and A, B, C, D, E and F digits.

Complete step by step solution:
Given that, in a city, the bus route numbers consist of natural numbers less than 100.
It means there are 99 routes.
But one more condition is that they are followed by one of the letters A, B, C, D, E, and F.
Thus each letter will take 99 routes with it.
So, different bus routes will be
\[\begin{gathered}
   = total{\text{ }}numbers{\text{ }}less{\text{ }}than{\text{ }}100\; \times all{\text{ }}letters \\
   \Rightarrow 99 \times 6 \\
   \Rightarrow 594 \\
\end{gathered} \]
For example, A1, A2, A3,…..A99 .This continues with letter B, C, D, E, and F.

Additional information:
1) All numbers starting from 1 up to infinity are called natural numbers.
2) Natural numbers including zero together form whole numbers.
3) All-natural numbers, zero and all negative numbers together are called integers.

Note:
1) The student should not consider 0 and negative numbers because though they are less than 100 they are not natural numbers.
2) Their consideration will give you infinite possible outcomes.