Applied Test Series

Question

The number of possible ways in which 5 identical helicopters can take off given that we are having 5 helipads.____

 

Answer 1

A case of Indistinguishable Object and Distinct Boxes (IODB) / Star – Bar problem

Suppose here helicopters are objects ( r ) and helipads are boxes ( n)

So, number of possible ways= (n-1+r) C r = 5-1+5 C 5= 9C5= 126

Answer 2

n=5

r (identical helicopters)=5

n-1+rCr =9C5=126

Answer 3

We have 5 identical helicopters, but the helipads are different.

• The first helicopter can take off or not – 2 ways
• The second helicopter can take off or not – 2 ways and so on

Thus, we have 2^5 = 32 ways (no helicopter takes off is also a possibility)