Ways of Selecting 4 Letters from the Word "EXAMINATION"

To determine the number of ways to select 4 letters from the word "EXAMINATION," we can use the concept of combinations. In a combination, the order of the selected items does not matter, so we will not consider permutations.

Step 1: Count the total number of letters in the word "EXAMINATION."
The word "EXAMINATION" consists of 11 letters.

Step 2: Determine the number of ways to select 4 letters from 11.
To do this, we will use the formula for combinations, which is given by:

C(n, r) = n! / [(n - r)! * r!]

where n is the total number of items, and r is the number of items to be selected.

In this case, we want to select 4 letters from 11, so the formula becomes:

C(11, 4) = 11! / [(11 - 4)! * 4!]

Simplifying this expression, we have:

C(11, 4) = 11! / (7! * 4!)

Step 3: Calculate the combination.
Using the factorial function, we can calculate the combination as follows:

C(11, 4) = (11 * 10 * 9 * 8 * 7!) / (7! * 4 * 3 * 2 * 1)

C(11, 4) = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1)

C(11, 4) = 11 * 10 * 9 * 8 / 4 * 3 * 2 * 1

C(11, 4) = 330

Therefore, the number of ways to select 4 letters from the word "EXAMINATION" is 330.

Answer: A. 330