Question

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

Answer 1

Complete Question

Lena is putting 11 colored light bulbs into a string of lights. There are 3 white light bulbs, 4 yellow light bulbs, and 4 red light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?

Answer:

The value is $N = 11550 \ distinct\ orders$  

Step-by-step explanation:

  The total number of bulbs  is $n = 11$

   The number of white bulbs is  $n_w = 3$

  The number of yellow bulbs is  $n_y = 4$

   The number of  red bulbs  is  $n_r = 4$

Generally the number of  distinct order of light bulbs there are if two light bulbs of the same color are considered identical is mathematically represented as

     $N = \frac{n!}{ n_w ! n_y! n_r!}$

=> $N = \frac{11!}{ 3 ! 4 ! 4!}$

=> $N = \frac{11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 }{ 3 * 2 * 1 * 4 * 3* 2 * 1 * 4 * 3* 2 * 1 }$  

=> $N = 11550 \ distinct\ orders$