- #1
leo255
- 57
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Thread moved from the technical math forums, so no HH Template is shown.
- Find the number of subsets of S = {1,2,3,...,10} that contain
(a) the number 5.
(b) neither 5 nor 6. - (c) both 5 and 6.
- (d) no odd numbers.
- e) exactly three elements.
- (f) exactly three elements, all of them even.
- (g) exactly five elements, including 3 or 4 but not both. (h) exactly five elements, but neither 3 nor 4.
- (i) exactly five elements, the sum of which is even.
- 2. Let A be the set of all strings of decimal digits of length seven. For example 0031227 and 1948301 are strings in A.
- (a) Find |A|.
- (b) How many strings in A begin with 1237 (in this order)?
- (c) How many strings in A have exactly one 3?
- (d) How many strings in A have exactly three 3s?
So, I'm trying to figure out the difference between what these two questions are asking (I am studying for a final next week).
I know that the answer to the first question is 10^9 and 10^7, respectively.
The answer to part b and c for the first question is 10^8. For c in the 2nd question, I would assume that the answer would be 10^6, but that is wrong. The answer is 7*(9^6). Also, for part d, the answer is C(7, 3) * 9^4, and I don't quite see how that is gotten.
Thanks for looking.