Problem 1:

A special box is designed. It has ten sides. The numbers from 1 to 10 are written on the ten sides of the box in one fixed order.( Just like how the numbers on a dice are in one configuration only).

Now the box is rolled six times. The number on the top face of the box when it is rolled is the number we choose. What is the probability that the numbers we choose (i.e. numbers on top face) on each of 2nd , 3rd,4th,5th and 6th tries is at least 1 greater than the number we choose on the previous try. That is the number on 2nd try should be greater than number on 1st try, number on 3rd try should be greater than the number on the 2nd try and so on till the last try.

Problem 2:

Calculate the number of different vote totals, using the cumulative voting method when there are m candidates, n voters, l open seats, and each voter need not vote.

Problem 3:

Write down all the distributions of:

(a)     3 distinguishable balls a,b,c into 2 distinguishable cells 1,2

(b)     4 distinguishable balls a,b,c,d into 2 distinguishable cells 1,2

(c)     3 indistinguishable balls a,a,a into 2 distinguishable cells 1,2

(d)     4 indistinguishable balls a,a,a,a into 2 distinguishable cells 1,2