Permutation License plate problem

Answer C would be correct if we were looking for the number of different ways to arrange the 36 characters with the requirement that each be unique. It comes from the permuation formula:

(n P r) = (n!)/(n-r)!

which gives the number of ways to different ways to pick r objects from a set of n, where the order of the r objects selected matters. So, this would be correct if we were asked how many license plates would be possible if each letter/number could only appear once on each plate.

However, in this question, there is nothing to state that the license plate AAAAAA could not be used. Therefore, there are 36 choices for the first character, 36 for the second, and so on. The total number of license plates is then 36*36*36*36*36*36.

Hope that helps answer your question.

But the question says that the license plate is a COMBINATION of letters and numbers. Doesnt that mean that the AAAAAA option isnt really an option?

Thanks for the explanation, hopefully I wont choose to go with my reasoning on the actual day.

Guys,

The key here is to note that the nPr and nCr formulas only apply when there is replacement. (That is why the factorial term is used).

Example 1: How many license plate combinations are there if you can use all 36 letters and nos, but you can only use one letter or number once and the order of the letter and nos matters?

Here, because there is no replacement (ie you can only use one letter or number once) and because the order matters you must use nPr.

Example 2: How many license plate combinations are there if you can use all 36 letters and nos, but you can only use one letter or number once and the order of the letter and nos does not matter?

Here, use nCr.

Example 3: How many license plate combinations are there if you can use all 36 letters and nos, order matters, and you can use letters and nos twice?

Here you us 36^n.