Chapter 13.2, Problem 30STP

To determine

To find: the probability that the letter spell GEOMETRY if the letter is randomly selected.

Answer to Problem 30STP

The probability is $\frac{1}{20160}$ .

Explanation of Solution

Given:

The random selected from alphabet.

  

Concept used:

Number of different permutations of $n$ objects where there are $n_1$ repeated items, $n_2$ repeated items,…. $n_k$ repeated items.

  $\frac{n!}{n_1!n_2!\mathrm{...}{n}_k!}$ .

The probability formula is used to compute the probability of an event to occur as:

  $P\left(A\right)=\frac{\text{Number of favorable outcome}}{\text{Total Number of favorable outcomes}}$ .

Calculation:

There are  $8$ letters in which only  $E$  appears twice and the others once each. So, the number of distinguishable permutations is:

  $\frac{8!}{7\left(1!\right)\times 2!}=20160$ .

The total number of possible outcomes is  $20160$  and there is only one favorable outcome which is $GEOMETRY$ . Therefore, the probability is:

  $\frac{1}{20160}$ .

Hence, the probability is $\frac{1}{20160}$ .