Question

Ten different letters of an alphabet are given. 2 of these letters followed by 2 digits are used to number the products of a company. In how many ways can the products be numbered?

• A. 52040
• B. 8100
• C. 5040
• D. 1000
• E. 4000

Hint:

For letters and digits in sequence, treat each block separately and multiply permutations.

Answer 1

The Correct Option is B

Step 1: Select letters.
2 letters from 10 distinct letters, order matters: \[ {}^{10}P_{2} = 10 \times 9 = 90 \]
Step 2: Select digits.
Digits from 0–9 (10 digits), order matters, no repetition: \[ {}^{10}P_{2} = 10 \times 9 = 90 \]
Step 3: Multiply.
Total product numbers = \(90 \times 90 = 8100\).
Final Answer:
\[ \boxed{8100} \]