Question

A machinist produced 22 items during a shift. Three of the 22 items were defective and the rest were not defective. In how many different orders can the 22 items be arranged if all the defective items are considered identical and all the nondefective items are identical of a different class?

Answer 1

Answer: There are 1540 different orders.

Step-by-step explanation:

• The number of ways to arrange n things where 'a' things are alike and 'b' things are a like and so on...

                              $\dfrac{n!}{a!\ b!\ ....}$

Given : Total items = 22

Defective items = 3

Not defective items = 22-3 = 19

Then, the number of different orders can the 22 items be arranged if all the defective items are considered identical and all the non-defective items are identical of a different class :

$\dfrac{22!}{3!\times19!}\\\\=\dfrac{22\times21\times20\times19!}{6\times19!}=1540$

Hence, there are 1540 different orders.