Question

How many 3-letter words can be formed from the letters of the word 'OBJECTS' if repetition is not allowed?

• A. 35
• B. 120
• C. 210
• D. 840

Answer 1

The Correct Option is D

To determine how many 3-letter words can be formed from the letters of the word 'OBJECTS' without repetition, we start by noting the total number of unique letters. 'OBJECTS' consists of 7 distinct letters: O, B, J, E, C, T, S.

The formula for permutations, where no repetition is allowed, is given by:

P(n, r) = n! / (n-r)!

where n is the total number of items to choose from, and r is the number of items to choose.

In this problem, n = 7 (the total number of unique letters) and r = 3 (since we are forming 3-letter words).

Substituting these values into the formula, we have:

P(7, 3) = 7! / (7-3)! = 7! / 4!

Calculate 7! and 4!:

• 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
• 4! = 4 × 3 × 2 × 1 = 24

Now, divide 5040 by 24:

7! / 4! = 5040 / 24 = 210

Thus, the total number of 3-letter words that can be formed is 210.

In conclusion, the correct answer is 210, not 840 as mentioned earlier in the options.