In how many different ways can you put20 balls of the same colour into two numbered box
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Consider the 1st box and choose how many balls we put into this box. We can put 0, 1, 2, ..., 20 balls - 21 options.
All another balls we put into 2nd box.
These are all ways to put 20 balls of same colour into two numbered box - 21 ways.
Answer: 21 ways.