Question

The number of ways in which four letters can be selected from the word 'DEGREE', is

• A. 7
• B. 6
• C. \(\frac{6!}{3!}\)
• D. None of these

Hint:

Handle selections with identical objects by considering cases based on the number of identical letters chosen.

Answer 1

The Correct Option is A

To determine the number of ways in which four letters can be selected from the word "DEGREE", we first analyze the composition of the word:

• The word "DEGREE" consists of six letters.
• The letters in "DEGREE" are: D, E, G, R, E, E.
• Notably, the letter 'E' is repeated three times.

To solve this, we need to consider cases based on the number of times 'E' is selected:

1. Case 1: No 'E' selected:

Possible selection of 4 letters: D, G, R (Only 3 letters available, so not possible)

1. Case 2: One 'E' selected:

Select 3 more letters from D, G, R. There is only one way: D, G, R

1. Case 3: Two 'E's selected:

Select 2 more letters from D, G, R:

• Possible selections: D, G; D, R; G, R (3 ways)

1. Case 4: Three 'E's selected:

Select 1 more letter from D, G, R:

• Possible selections: D; G; R (3 ways)

Adding these possibilities together, we calculate the total number of ways:

\(1 + 3 + 3 = 7\)

Therefore, the total number of ways to select four letters from "DEGREE" is 7.

This matches the given correct answer option.