You are thinking of using some leftover ceramic tiles to make a decorative border for a patio. You have ten blue, four gold, and six white tiles. In how many ways can you make the border if it requires 15 tiles and you use only blue and white ones? Explain your reasoning.

Question

You are thinking of using some leftover ceramic tiles to make a decorative border for a patio. You have ten blue, four gold, and six white tiles. In how many ways can you make the border if it requires 15 tiles and you use only blue and white ones? Explain your reasoning. 
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Reiny · Answer

number of ways to choose: 6W,9B 5W,10B Number of ways to arrange 6W,9B = (15!/6!9!) = 5005 number of ways to arrange 5W,10B = 15!/(5!10!) = 3003 total number of ways = 5005+3003 = 8008