If Vahin randomly selected a permutation of the letters A, A, C, C, L, L, O, R, T, U, what is the probability he would spell “calculator”?

Answer 1

We're talking about permutations, so order matters and there's no replacement. The formula for permutations, P(n, r) is given by n! / (n-r)!.

We have 10 letters so n=10 and each permutation has 10 letters, so r-10, which makes the formula:

10! / (10-10)! = 10! / 1 = 3628800.

so the probability of each permutation is 1/3628800.

However, there are 2 As, 2 Cs, and 2 Ls. That means there are several different permutations of those letters alone that still spell 'Calculator.' Looking at just those 6 letters (n=6, r=6) to get the possible permutations, we have

6!/(6-6)! = 720.

So the probability of a permutation spelling 'Calculator' is actually 720/3628800 or 1/5040.

Hope that helps!