MAT 375-1

HOMEWORK ASG. #9

HAND IN TUESDAY, NOVEMBER 23

For problems #1-4, construct an appropriate exponential generating function, and calculate the desired coefficient without the aid of Maple.

1. Use an exponential generating function to find the number of 8-letter sequences formed from A’s, B’s and C’s that contain at least one A.

2. Exercise Set 6.4 #6

3. Use an exponential generating function to find the number of ways to distribute n different objects into 5 different boxes so that there is an even number of objects in box #5.

4. Use an exponential generating function to find the number of ways to make a single stack of n poker chips (of three possible colors—red, white or blue) that contains an odd number of red chips and at least one blue chip.

For problems #5-7, construct a recurrence relation model for the problem, and then calculate the desired term of the sequence with Maple.

5. How many ways are there to climb 15 steps by taking one, two or three steps with each stride?

6. How many ternary sequences of length 10 contain no pair of consecutive zeros?

7. How many ways are there to make a single stack of 12 poker chips (of three possible colors—red, white or blue) so that:

a) no adjacent chips have the same color?

b) no red chip appears anywhere in the stack above a blue one?