Chapter 11.6, Problem 43E

To determine

To calculate: thedifferent permutation of three letters of ball drawn from the hat.

Answer to Problem 43E

the different permutation of three letters of ball drawn from the hat is $12$ .

Ans of option a is less than $P{}_3$

Explanation of Solution

Given :

Word= ball

Calculation :

1. for find the different permutations of three letters we have to choose three cards from four cards, to do that we use permutation formula. But both l are same so we have to divide the result by 2!.

  $\begin{array}{l}P{}_3=\frac{4!}{\left(4-3\right)!}\text{ [substitue n by 4 and r by 3]}\\ P{}_3=\frac{4!}{1!}\text{ [subtract]}\\ P{}_3=24\text{ [expand factorial and multiply]}\end{array}$

Different permutations = $\frac{24}{2!}$

= $12$

2. Ans of option a is less than $P{}_3$ because both L are identical so whatever L we chose both are same, therefore some time some conditions are same so we remove the same conditions.

Hence,

a.the different permutation of three letters of ball drawn from the hat is $12$ .

b. Ans of option a is less than $P{}_3$