Question

how many combination are there in addition

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Answer 1

Answer:

This problem is equivalent to finding the number of integer solutions to a+b+c+d+e=10.

If you imagine your 10 as a line of 10 stars then you can insert 4 "+" signs in between the stars to get a solution, for example +⋆⋆+⋆⋆⋆⋆+⋆+⋆⋆⋆ represent the solution 0+2+4+1+3.

Since every permutation of stars and "+" signs represents a solution the total number of solutions is given by the possible permutations of this 14 symbols, that is 14!10!4!. The same method, which is usually called stars and bars can be used for similar problems with other numbers involved.

Edit: in the case of 3 numbers adding up to 10 stars and bars gives 12!10!2!=66 as answer, you have 63 because you didn't count the 3 triplets with 2 zeros and a ten, was that intended?

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

our wish so many combination are there in addition.

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