Question

Ten different letters of an alphabet are given. Words with 6 letters are formed with these alphabets. How many such words can be formed when repetition is not allowed in any word?

• A. 52040
• B. 21624
• C. 182340
• D. 151200
• E. 600000

Hint:

“Words with no repetition” → always a permutation problem: \({}^{n}P_{r} = \frac{n!}{(n-r)!}\).

Answer 1

The Correct Option is D

Step 1: Choose and arrange 6 letters from 10.
Since repetition not allowed, this is permutation: \[ {}^{10}P_{6} = \frac{10!}{(10-6)!} = \frac{10!}{4!} \]
Step 2: Calculate.
\[ 10! = 3628800, \quad 4! = 24 \] \[ \frac{3628800}{24} = 151200 \]
Final Answer:
\[ \boxed{151200} \]