Chapter 12.6, Problem 52PPE

To determine

To calculate: The number of arrangements of letters taken three at a time that can be formed from each set of cards.

Answer to Problem 52PPE

There are $24$ arrangements of letters.

Explanation of Solution

Given information:

  

Formula used:

A permutation is an arrangement of objects in a specific order. The expression $P{}_r$ represents the number of permutations of $n$ objects arranged $r$ at a time.

  $P{}_r=\frac{n!}{\left(n-r\right)!}$

For any positive integer $n$, the expression $n$ factorial is written as $n!$ and is the product of integers from n down to 1.

Calculation:

According to the question ,

There are 4 cards, each card marked with the letter $\text{M,N,O and P}$ respectively.

Using permutations we get,

  $\begin{array}{l}P{}_3=\frac{4!}{\left(4-3\right)!}\\ =\frac{4!}{1!}\\ =\frac{4\times 3\times 2\times 1}{1}\\ =4\times 3\times 2\\ =24\end{array}$

Hence, there are $24$ arrangements of letters.