Q3.

Five people stand at the vertices of a pentagon, throwing frisbees to each other. They have two frisbees, initially at adjacent vertices as shown in the figure. In each time interval, each frisbee is thrown either to the left or to the right (along an edge of the pentagon) with equal probability. This process continues until one person is the target of two frisbees simultaneously, then game ends. (Note : All throws are independent of past history) Find the mean and variance of the number of pairs of throws.

Q4.

A rod is divided into six segment is to be colored with one or more of 4 different colors. In how many ways can this be done ?

Q5.

A committee is to be selected from 5 candidates a, b, c, d and e. The selection must satisfy all the following conditions : 

• Either a or b must be included, but not both

 • Either c or e or both must be included 

• If d is included then b must be included 

• Either a or c are included or neither is included. 

• If e is included, then c and d must be included. How should selection be made ?