9. You have to place n balls in m ( m > n ) cells. Find the probability that a given cell contains exactly k -balls in the following cases:

 

 (i) The balls are undistinguishable
( Bose-Einstein statistics )

 (ii) The balls are distinct
( Boltzmann Maxwell distribution )

 (iii) The balls cannot be distinguished and at most one ball is allowed in a box.

10. An electric circuit looks as in Fig. 1, where the numbers indicate the probability of failure of various links which are all independent. What is the probability that the circuit is in operation?