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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)?

Respuesta :

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:

[tex]N=\frac{n!}{n_g!n_{y!}n_r!}[/tex]

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:

[tex]\begin{gathered} N=\frac{11!}{5!4!2!} \\ N=\frac{11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!\cdot24\cdot2} \\ N=11\cdot10\cdot9\cdot7 \\ N=6,930 \end{gathered}[/tex]

So, Ahmad has 6,930 distinct orders

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