A sales clerk must createa display of china plates. She has 6 blue plates, 5 white plates, and 5 patterned plates. In how many distinguishable ways can she arrange the plates?

 

Answer:

she can arrange the plates in 2018016 distinct ways

Step-by-step explanation

We are given that She has 6 blue plates, 5 white plates, and 5 patterned plates.

So total number of plates is 5+5+6=16

So total way to arrange them is 16!

As all plates are not distinct

So these are not all distinct ways

now

to find the distinct arrangement we have to use the Multinomial Theorem

The Multinomial Theorem says in order to count the number of distinct ways a set of elements with duplicate items can be ordered all you need to do is divide the total number of permutations by the factorial of the quantity of each duplicate

We are given that

She have

Blue plate duplicated 6 times

White plate duplicated 5 times

Patterned plate duplicated 5 times

So

total number of permutation? ?/ factorial of quantity of each duplicate

distinguishable ways to arrange the plate=?16!/6!5!5!??

=2018016