Hi, I'm a student. I'll appreciate if someone can help me to solve the following:
1.a.Find a recurrence relation for the number of n-digit binary sequences with no pair of consecutive 1's b. repeat for n digit trenary seq. c. repeat for n digit trenary seq. With no consecutive 1's or conse' 2's.
2. find a recurrence relation for the number of bees in the nth previous generation of a male bee, if a male bee is born asexually from a single female and a female bee has the normal male and female parents. F(1)=1 f(2)=2 f(3)=3
3. find a recurrence relation for the number of regions created by n lines on a piece of paper if k of the lines are parallel and the other (n-k) lines intersect all other lines (no three lines intersect at one point).
4.a switching game has n switches, all initially in the OFF position. In order to be able to flip the ith switch, the (i-1)st switch must be ON and all the earlier switches OFF. The first switch can always be flipped. Find a recurrence relation for the total number of times the n switches must be flipped to get the nth switch ON and all the others OFF.
5. find a recurrence relation for the number of distributions of n identical objects into k distinct boxes with at most four objects in a box and with exactly m boxes having four objects.
6.find a system of recurrence relations for computing the number of n digit binary sequences with an even number of 0's and an even number of 1's.
7. find a system of recurrence relations for computing the number of n digit binary sequences with: a. an even number of 0's b. an even total number of 0's and 1's
8. a wizard has 5 friends. During a long wizard's conference, it met any given friend at dinner 10 times, any given pair of friends 5 times, any given threesome of friends 3 times, and given foursome 2 times, and all five friends together once. If in addition it ate alone 6 times, determine how many days the wizard's conference lasted.
9. how many arrangments of 1,2,...n are there in which only the odd integers must be deranged(even integers may be in their own positions).