Question

How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?

• A. 360
• B. 720
• C. 840
• D. 1260

Hint:

Tip: Permutations without repetition are calculated using \( P(n,r) = \frac{n!}{(n-r)!} \).

Answer 1

The Correct Option is A

The word "BINARY" consists of 6 distinct letters. We need to find the number of different 4-letter words that can be formed from these letters without using any letter more than once.
Since the order in which we select the letters matters (because each arrangement represents a different word), this is a permutation problem.

A permutation is an arrangement of objects in a specific order. The formula to calculate permutations of selecting \(r\) objects from a set of \(n\) distinct objects is given by:
\[ P(n, r) = \frac{n!}{(n-r)!} \]
Here, \(n = 6\) (the letters B, I, N, A, R, Y) and \(r = 4\) (we are forming 4-letter words):
\[ P(6, 4) = \frac{6!}{(6-4)!} = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = 6 \times 5 \times 4 \times 3 \]
\[ = 360 \]
Thus, there are 360 different 4-letter words that can be formed from the letters of the word "BINARY" without repetition.

Answer 2

Step 1: Count letters  
The word "BINARY" has 6 distinct letters.

Step 2: Number of 4-letter words without repetition  
Number of ways = \( P(6,4) = \frac{6!}{(6-4)!} = \frac{6!}{2!} = \frac{720}{2} = 360 \) 

So the correct answer is (A) 360.