there are <u>3003 ways</u> to distribute six indistinguishable balls into nine distinguishable bins using combination formula
A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations. (It doesn't matter how each set's members are organized.)
A combination is made up of n distinct elements that are combined k at a time. The words k-selection and combinations where repetition is permitted It's common to employ k-multiset or k-combination with repetition. There would be three more 2-selections if it were possible to have two of any one type of fruit in the aforementioned example: one with two apples, one with two oranges, and one with two pears.
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