Chapter 6, Problem 23CT

To determine

To find the number of animals the wildlife preserve can identify with a one digit number and a capital letter and the number of animals they can identify using a two digit number and a capital letter.

Answer to Problem 23CT

The wildlife preserve can identify the animals with a one digit number and a capital letter in $260$ ways.

  $2340$ animals can be identified using a two digit number and a capital letter.

Explanation of Solution

Given information:

The given statement is:

“A wildlife preserve identifies each animal in the preserve with a one-digit number and a capital letter. How many animals can the preserve identify? How many animals can the preserve identify using a two-digit number and a capital letter?”

Calculation :

There are $10$ one-digit numbers from $\text{0 to 9}$ and $\text{26}$ letters in the English alphabet.

The number of ways the wildlife preserve can identify with a one digit number and a capital letter can be calculated by:

  $\begin{array}{l}10\times 26\left[\text{Using the multiplication principle}\right]\\ =260\end{array}$

Hence, the wildlife preserve can identify the animals with a one digit number and a capital letter in $260$ ways.

There are $90$ two-digit numbers and $\text{26}$ letters in the English alphabet.

The number of animals they can identify using a two digit number and a capital letter can be calculated by:

  $\begin{array}{l}90\times 26\left[\text{Using the multiplication principle}\right]\\ =2340\end{array}$

Hence, $2340$ animals can be identified using a two digit number and a capital letter.