suppose I have a list of numbers [1,2,3….20].In how many ways can i select three numbers with repetitions from this list
Can somebody explain how to solve this question .I thought about it and it seems to me that there are 20 identical objects of first type ,20 identical objects of second and of third and we have to select three items from the three types which gives me $$\binom{20}{1} X \binom{20}{1}X \binom{20}{1}$$.Is this correct?
Best Answer
If - as clarified in comments - the order does not matter the sequences differ only by counts of the corresponding items. This is equivalent to distributing 3 balls between 20 bins. The number of ways to perform this can be computed by stars and bars as: $$ \binom{3+20-1}3=\binom{22}3. $$