Question

A combination lock consists of the 26 letters of the alphabet. If a 3-letter combination is needed,find the probability that the combination will consist of the letters ABC in that order. The same letter can be used more than once. ( Note: A combination lock is a really a permutation lock.)

Answer 1

The probability of having letter A is (1/26), the probability of having B (1/26) and the probability of having letter C is (1/26)

We can only have one ABC in that order.

To find the total probability we have to multiply each of them.

So:

$\begin{gathered} \frac{1}{26}\lparen\frac{1}{26})\lparen\frac{1}{26}) \\ =\text{ }\frac{1}{17576} \end{gathered}$

The probability is 1/17576