Chapter 13.2, Problem 3CYU

To determine

To find: the probability that license plate using letters and numbers will be $CFF3133$ .

Answer to Problem 3CYU

The probability is $\frac{1}{420}$ .

Explanation of Solution

Given:

There are three letter which are:

  $C,F\text{ and }F$ .

There are three numbers as:

  $3,3,3\text{ and }1$ .

Concept used:

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  $3$  letters and  $4$ digits This is a permutation with repetition. There are total of  $7$  objects in which F appears twice and 3 appears three times. The number of distinguishable permutations is the total number of possible outcomes is  $420$ and there is only one favorable outcome which is $CFF3133$  Therefore, the probability is  $\frac{1}{420}$

Hence, the probability is $\frac{1}{420}$ .