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How many combinations of two-digit numbers having 8 can be made from the following numbers?

8, 5, 2, 1, 7, 6

  • a)
    10

  • b)
    6

  • c)
    9

  • d)
    11

Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
How many combinations of two-digit numbers having 8 can be made from t...
The possible two-digit numbers are: 88, 85, 82, 81, 87, 86, 58, 28, 18, 78, 68
These are 11 in number.
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Community Answer
How many combinations of two-digit numbers having 8 can be made from t...
To find the number of combinations of two-digit numbers with 8 that can be made from the given numbers (8, 5, 2, 1, 7, 6), we need to consider all possible arrangements of these numbers.

Step 1: Create all possible two-digit numbers using the given numbers.
Since we are looking for two-digit numbers with 8, the tens digit can only be 8, and the units digit can be any of the given numbers (8, 5, 2, 1, 7, 6). Therefore, the possible two-digit numbers are:

18, 58, 28, 88
48, 78, 68

Step 2: Count the number of two-digit numbers that have 8.
From the list above, we can see that there are a total of 7 two-digit numbers with 8.

Step 3: Determine the number of combinations.
To find the number of combinations, we need to consider the order in which the numbers are arranged. In this case, we are looking for all possible combinations of two-digit numbers with 8.

To count the combinations, we use the formula for combinations:

C(n, r) = n! / (r! * (n-r)!)

where n is the total number of items and r is the number of items chosen.

In this case, there are 7 two-digit numbers with 8 (n = 7) and we are choosing 2-digit numbers (r = 2). So the formula becomes:

C(7, 2) = 7! / (2! * (7-2)!) = 7! / (2! * 5!) = (7 * 6 * 5!) / (2 * 1 * 5!) = (7 * 6) / (2 * 1) = 42 / 2 = 21

So, there are a total of 21 combinations of two-digit numbers with 8 that can be made from the given numbers.

Step 4: Compare the result with the options.
The correct option is (d) 11. However, based on the calculations, the correct answer should be 21. Therefore, the correct answer might be a typographical error in the given options, and the answer should be (a) 21.
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How many combinations of two-digit numbers having 8 can be made from the following numbers?8, 5, 2, 1, 7, 6a)10b)6c)9d)11Correct answer is option 'D'. Can you explain this answer?
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