HW7MA375S10 - Due Thursday, March 4th

6.4 - 6, 8, 12, 16 | 7.1 - 12, 24, 30, 36, 42, 44, 46

Section 6.4

6.

does the order of winning numbers set matter?

I don't think so. Typically, in a lottery, it's just a combination of numbers, not a permutation. For example, the combination "5, 10, 15, 20, 25, 30" would be the same as "30, 25, 20, 15, 10, 5."

So would it just be the 1 over the number of ways that we can make a 5 bit string out of 50 numbers?

8.

12.

I figured out the probability, but got a little confused about the expectation. Any hints? thanks

Hint: it's a geometric distribution. See pages 433-434 - specifically, Theorem 4 on page 434.

16.

Section 7.1

12.

Is there really ANY way to do this with counting principles? If we look at the total number of bit strings of length n with 3 consecutive zeros, for n = 3, 4, 5, and 6, we see 1, 3, 8, and 20. (It's 0 for any n < 3, of course.) Is there really a pattern there? Even if you look at the increments, it goes +1, +2, +5, +12; there is no discernible pattern, unless I'm just missing it. Any help?

24.

30.

36. I'm totally lost, help please.

I broke down how many ways can 10 cents, 15 cents, and 20 cents be paid using tree diagram. Then, find the recurrence relation of a20 with respect to the others.

42.

Does anyone have any advice for this one?

44. any idea about showing f5n is divisible by 5?

46. i got 9 ways to parenthize x_0-x_4. is this correct because part B is confusing.

I don't think that's right. You can use the explicit formula in the example to find the correct number (part c).