Counting Problems?

Question

How many bit strings of length 6 or less are there?
My answer is 127.

How many strings are there of 4 letters that have the letter X in them?
My answer is 26^3.

I'm stuck on one question and would appreciate any help on it please.
How many subsets of set of 100 elements have more than 1 element?

Thank you very much!!

Answer 1

I feel like there is something that i am missing are you looking at a picture or something?

Answer 2

4 letters with X: Your answer doesn't take into account where the X can be. Nor does it deal with the more subtle point of overcounting with mulitple X's. I'd use the complement (which will come up below). There are 26^4 total 4 letter words. There are 25^4 4 letters words with no X. That leaves 26^4 - 25^4 = 66351 four letter words with at least one X.

For the last question, you'll looking at all possible subsets, of which there are 2^100 (choose "in or out" for each element to build a subset). Again, time for the complement: how many subsets have 0 or 1 element? Empty set and 100 singletons. So that leaves 2^100 - 101 subsets with more than 1 element (huge number, more than 10^30).

Answer 3

How many subsets of set of 100 elements have more than 1 element?

ur question is not that clear to me.i think that u have to specify the number subsets U CHOOSE/CHOSE to have.

btw for "How many strings are there of 4 letters that have the letter X in them?
My answer is 26^3.
>>>>that answer is only right if and only if REPETITION IS ALLOWED!!!!i.e iff u can have the same letter more than once in your string.if repetion wasnt allowed your answer would be 25*24*23 if the ORDERING is important OR 25*24*23 /3! if the ORDERING IS IRRELEVANT