Counting Definition and 413 Threads

How many 16-bit strings contain exactly nine 1's? I said the total number is 2 to the 16th power, so to get half with 1's would be 2 to the 8th, or 256. How many 16-bit strings contain at least fourteen 1's? I have no idea. When determining a how to get 2 pair in a poker hand, why is...

Hexadecimal numbers are made using the sixteen digits 0 - 9, A-F. how many hexadecimal numbers are there between the hexadecimal numbers 30 and AF? There are 8 numbers between 3 and A, so I got 3 x 16, but I don't really know.

I can't seem to put the Fundamentals of Counting to good use... I have such a hard time answering probability questions with the rules of counting. Here's one question that blew my mind: There are 4 persons. The sample space E consists of the events E={E1, E2, E3, E4, E5 }. Let E1 be the...

in this postcrpit i would like to say i have fund a second order integral equation (fredholm type) for the prime number counting function in particular for Pi(2^t)/2^2t function being Pi(t) the prime number counting function,teh equation is like this is we call Pi(2^t)/2^2t=g(t) then we have...

Here's an old one: starting with 0 (or 1) list all the natural numbers using nothing but 4 4s. I'll go first. 0 = (4 - 4)/(4*4) 1 = (4*4)/(4*4) 2 = (4*4)/(4*sqrt(4)) ... etc

The question is how many 8-bit strings have either the second or the fourth bit 1 (or both)? I know the soulution is 3*2^6 but why?? Also this question how many 8 bit strings begin and end with 1? is it 8C2?

Having a lot of trouble with this problem as well: How many integers less than 500 are relatively prime to 500? I know that when two numbers are relatively prime, that means that the greatest common divisor of those two numbers is 1. But I can't figure out a formula that uses sets in order...

I have some questions about counting principles in mathematics: If I had standard deck of 52 playing cards, then a. How many ways can one draw a heart or a spade? b. " " an ace or a king? c. " " a card numbered 2 through 10? d. " " a card numbered 2 through 10 or a king? I got these answers...

I think i got this answer. How many ways are there to distribute five distinguishable objects into three indistinguishable boxes? Wouldn't the answer just be C(5,3) because the boxes are indistinguishable? Or do i treat this question the same as if the boxes were distinguishable?

A general two digit counting number is: d1*b + d0 = C ; where C is the count Let b = 2 as an example d 1 0 C ------ 0 0 0 0 1 1 1 0 2 1 1 3 b is the count of symbols in the digit, but it can start at 0 d1*0 + d0 = C ; works fine d0 = C ; and can be any base. d 1 0 C...

The dial on a 3 number combination lock contains markings to represent the numbers from 0 to 59. How many combinations are possible if the first and second numbers differ by 3? What I did was: 1st number: It can be any of the 60 numbers (if we take 0 also as a #) 2nd number: I think since...

is there an easier way of knowing how to count certain sequences in a problem using the same concept, i mean there are formulas but how do we tell which one we should use.

Hello all! First of all, please excuse me for barging in on you all like this. I am a nobody with little formal education in ANY field and I apologize if I seem a little mad. The bottom line is this - I just CANNOT find any satisfactory answers to my questions across the whole of the net and...