If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to:

Step-by-step solution

Given, Rooms are identical, So, total ways to distribute 5 employees into 4 rooms are: 5 , 0 , 0 , 0 ⇒ 1 way 4 , 1 , 0 , 0 ⇒ 5 ! 4 ! = 5 ways 3 , 2 , 0 , 0 ⇒ 5 ! 3 ! 2 ! = 10 ways 2 , 2 , 0 , 1 ⇒ 5 ! 2 ! 2 ! 2 ! = 15 ways 2 , 1 , 1 , 1 ⇒ 5 ! 2 ! 1 ! 3 3 ! = 10 ways 3 , 1 , 1 , 0 ⇒ 5 ! 3 ! 2 ! = 10 ways Total ⇒ 1 + 5 + 10 + 15 + 10 + 10 = 51 ways