Chapter 12.CT, Problem 1CT

List all the ways you can select two different letters from the word EXIT. The order of selection is important, so IT is different from TI.

To determine

To find:

The list of all the ways that two different letters from the word EXIT and not giving importance to the order of selection.

Answer to Problem 1CT

Solution:

The following set gives the pair of selection of two different letters, $\left\{\text{EX, EI, ET, XE, XI, XT, IE, IX, IT, TE, TX, TI}\right\}.$

Explanation of Solution

1) Approach:

Systematic counting is the simplest way in which we count a set to list all possibilities.

2) Calculation:

Given,

The two different letters form the word EXIT.

$\text{W=}\left\{\text{EXIT}\right\}$

Here, we donate the choices by the letters $\text{E, X, I, T}\text{.}$

Draw a tree diagram with four branches as such we have four letters, which is the step 1 of the tree diagram as shown below.

Now, attach three branches to each of the branch obtained in step 1 as repetition is not possible.

Thus, it clear from the above tree diagram that these four letters can be selected in 12 ways as we have 12 branches in the final step of the tree diagram.

$\left\{\text{EX, EI, ET, XE, XI, XT, IE, IX, IT, TE, TX, TI}\right\}.$