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How many ways are there to select 8 coins from a piggy bank with 100 pennies and 80 nickels ?

Ans. C(2+8-1,8)

Suppose the Question had been :-

How many ways are there to select 8 coins from a piggy bank with 6 pennies and 6 nickels?

Now what would have been the answer?

C(2+8-1,8) will be wrong here because initally there were lot of coins in both classes so i could choose atleast one of then from both But in this case what should be the answer ?

Should i calculate manually ?

2 penny , 6 nickel

3 penny , 5 nickel

and so on...    But for a large number it would be a problem so how to do it ?

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