Combinations with Repetition

         

A bakery sells three kinds of pastries: donuts, muffins, and cookies. If you go to the store to buy 2828 pastries, how many different combinations of them can you buy if they only have 2727 of each type available?

Details and assumptions

All the pastries of one type are indistinguishable.

For his reverse birthday party, George is giving away bags with toys in them. If the party store sells 4 different toys and George is making 99 bags, each with a single toy in it, how many different combinations of toys can George make?

How many ways are there to choose distinct numbers a,ba, b and cc where a<b<c a < b < c from among the integers {1,2,,110}\{1, 2, \ldots, 110\} such that a+b+ca+b+c is an even number?

Cards for a trading card game can be purchased in packages of 6 cards, of which exactly 1 of them is a rare card.

If there are a total of 8 rare cards that can be collected, and you purchase 33 packages of cards, how many different combinations of the rare cards could you end up with?

For example, you could have 1 of the second rare cards, and the rest are the eighth rare card.

You have 6 identical balls and 6 (distinct) boxes numbered 11 through 6.6. How many ways can the 6 balls be distributed amongst the boxes?

Details and assumptions

Some of the boxes can be empty.

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