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

ANS CHOICES ARE
52040
8100
5040
1000
4000

According to the stated question, the conditions are:

The (serial) numbers are produced by two (distinct) letters ("two of these letters") followed by (any) two digits (0-9), then the number of ways products can be numbered will be:

first letter : 10 ways
second letter: 9 ways
first digit: 10 ways
second digit : 10 ways
Total=10*9*10*10=9000 ways.

If the two digits are to be distinct (which has not been specified), then there are 9 ways for the second digit and the total is 8100.

Well, it seems like a clownish question to me! Let's see if I can tickle your funny bone while providing an answer.

If there are ten different letters of an alphabet, we can assume they are the fun alphabet of clowns. So, let's imagine these clowns are creating product numbers!

Now, we are told that 2 of these letters are followed by two digits. That means, for each of those 2 letters, we have 10 options for the first digit (0 to 9) and 10 options for the second digit (again, 0 to 9).

Therefore, the total number of ways the product can be numbered is 10 options for the first letter, 10 options for the second letter, 10 options for the first digit, and 10 options for the second digit. This gives us a total of 10 × 10 × 10 × 10 = 10,000.

Ah, but don't forget that we only have 2 letters followed by two digits, so we need to divide our result by 2! (Clowns are very good at math, you know!)

So, the correct answer is 10,000 divided by 2, which gives us 5,000.

Hmm, none of the answer choices are an exact match for my clowny calculation. But I'll go with the closest one - 5040! It's only 40 away from my answer, but hey, close enough for a clown, right?

So, my final answer is 5040! I hope it made you smile, even if I had to juggle a bit with the numbers!

To find the number of ways the product can be numbered, we need to consider the following:

1. The first letter can be any of the ten different letters given.
2. The second letter can also be any of the ten different letters given.
3. The first digit can be any digit from 0 to 9.
4. The second digit can also be any digit from 0 to 9.

So, the total number of ways the product can be numbered is:

10 (options for the first letter) * 10 (options for the second letter) * 10 (options for the first digit) * 10 (options for the second digit)

= 10 * 10 * 10 * 10

= 10,000

Therefore, the answer is 10,000. None of the given answer choices match the correct answer.

To answer this question, we need to break it down into smaller steps:

Step 1: First, we need to select 2 letters from the given 10 letters of the alphabet. This can be done using the combination formula, which is represented as "nCr" (combination of n items taken r at a time). The formula for combination is: nCr = n! / (r! * (n-r)!). Here, n = 10 (total number of letters) and r = 2 (number of letters to be selected).

Step 2: Once we have selected 2 letters, we need to number the product. We are given that the product is numbered using two digits.

Step 3: We need to calculate the number of ways to number the product. Since there are 2 digits, each digit can take values from 0 to 9. Therefore, the number of ways to number the product is 10 * 10 = 100 (10 possibilities for the first digit and 10 possibilities for the second digit).

Step 4: Multiply the results of steps 1 and 3 to get the total number of ways to number the product.

Now, let's calculate the answer:

Step 1: 10C2 = 10! / (2! * (10-2)!) = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45

Step 2: There are 100 ways to number the product.

Step 3: Multiply 45 (from step 1) by 100 (from step 3):

Total number of ways = 45 * 100 = 4500

Therefore, the correct answer is not one of the given options. The correct answer is 4500.