Chapter 13.9, Problem 25PPS

To determine

To Find: Probability of the paper.

Answer to Problem 25PPS

The probability of the word begins with $d$ is $\frac{1}{5}$ .

Explanation of Solution

Given information:

  $P$ (Word begins with $d$ )

Calculation:

Total number of words is $5$ .

Thus, the total numbers of arrangements in the word “dream” $=5!$

  $\begin{array}{l}=5\times 4\times 3\times 2\times 1\\ =120\end{array}$

So, total number of cases are $120$ .

As the first alphabet is fixed in the word dream, that is $d$ .

Remaining alphabets are $4$ .

So, favorable number of cases for selecting word begins with $d$

  $=4!$

  $\begin{array}{l}=4\times 3\times 2\times 1\\ =24\end{array}$

So for calculating the probability that the word begins with $d$

  $P$ (Word begins with $d$ ):

  $\begin{array}{l}=\frac{favourablenumberofcases}{Totalnumberofcases}\\ =\frac{24}{120}\\ =\frac{1}{5}\end{array}$