Question

Ahmad is putting 11 colored light bulbs into a string of lights. There are 5 green light bulbs, 4 yellow light bulbs, and 2 red light bulbs. How many distinct ordersof light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?

Answer 1

So, we have a total of 11 light bulbs. 5 are green, 4 are yellow and two are red. In cases in which the light bolbs are considered identical, we use the following math formula:

`N=(n!)/(n_g!n_(y!)n_r!)`

In which n is the total, 11. ng is thee number of green lightbulbs, ny the number of the yellow ones, and nr the number of the reds. So:

`\begin{gathered} N=(11!)/(5!4!2!) \\ N=(11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5!)/(5!\cdot24\cdot2) \\ N=11\cdot10\cdot9\cdot7 \\ N=6,930 \end{gathered}`

So, Ahmad has 6,930 distinct orders