18 In some Problem of occupancy theory we are concerned with

1.8 In some Problem, of occupancy theory we are concerned with the number of way in which certain distinguishable objects can be distributed among individuals urns, boxes or cells. Find an expression for the number of ways in which distinguishable objects can be distributed among n cells, and use it to find the number of ways in which three different books can be distributed among the 12 students in an English literature class.

Solution

The expression is nCr = n!/[(n-r)!*r!]

In this case n=12, r=3

12C3 = 12!/[(12-3)!*3!]

= (12*11*10)/(1*2*3)

= 2*110

= 220