Question

The Farm Agency is to use only the letters A, B, and C to make tags. Let y be the number of tags they can make using n spaces. What is the formula for the number of tags they can make?

Answer 1

The formula for the number of tags they can make is y = 3^n

Answer 2

y=
`3^(n)`

Explanation:

There are three letters A, B, C in order to make the tags and y is the number of tags that can be made using n spaces. So, there are three choices for the first letter A and three choices for the remaining two letters that are B and C respectively.

By the basic counting principle,

Formulae for the number of tags they can make using n spaces is: 3×3×3×3×..........×3( n times)

=
`3^(n)`

Therefore, y=
`3^(n)`