Set S contains the elements = { 1, 2, 3, 4, 5, 6, 7, 8}. From this set, John takes sets of 6-digits each and sums all the possible 6-digit numbers that can be formed with those sets. What is the HCF of all these sums?

To find the highest common factor (HCF) of all the sums of 6-digit numbers that can be formed with sets taken from Set S, we need to first find all the possible 6-digit numbers that can be formed.

From Set S = {1, 2, 3, 4, 5, 6, 7, 8}, we can see that there are 8 elements.

To find the number of sets of 6 digits we can form, we need to calculate the combination. We can use the formula for combination, which is given by nCr = n! / (r!(n-r)!), where n is the number of elements and r is the size of the subsets.

In this case, we need to find 6-digit numbers, which means r = 6. So, nCr = 8C6 = 8! / (6!(8-6)!) = 8! / (6!2!) = 8 x 7 / (2 x 1) = 28.

So, there are 28 sets of 6 digits that can be formed from Set S.

Next, we need to calculate the sum of all the possible 6-digit numbers that can be formed with these sets.

Since we are considering all the possible combinations, we need to find the sum of all the numbers formed by taking each digit from each set.

To calculate the sum, we can start by finding the sum of all the numbers formed by using the first digit from each set. This sum will be equal to the sum of the first digit (1+2+3+4+5+6+7+8) multiplied by the number of combinations (28).

So, the sum of the numbers formed using the first digit from each set = (1+2+3+4+5+6+7+8) x 28.

Similarly, we can calculate the sum of the numbers formed using the second digit from each set, the third digit from each set, and so on.

Finally, to find the HCF of all these sums, we need to calculate the HCF of all the individual sums.

You can calculate the HCF of these sums using the Euclidean algorithm or by finding the prime factors of each sum and finding their common factors.

Once you find the HCF of all these sums, you will have the answer to your question.