Chapter 13.2, Problem 11PPS

To determine

To find: the probability of getting word BASKETBALL from random selected of the letters.

Answer to Problem 11PPS

The probability is $\frac{1}{453600}$ .

Explanation of Solution

Given:

Santiago bought some letter magnets.

  

Concept used:

The number of ways of arranging $n$ item in order $=n!$ .

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 $10$ letters in which $A,B\text{ and }L$ each appear twice. The number of distinguishable permutations is:

  $\frac{10!}{2!\times 2!\times 2!}=453600$ .

The total number of possible outcomes is $453600$ and there is only one favorable outcome which is BASKETBALL. Therefore, the probability is $\frac{1}{453600}$ .

Hence, the probability is $\frac{1}{453600}$ .