Solving 6 1s and 8 0s Bit Strings

  • Thread starter meatspin
  • Start date
  • Tags
    Counting
In summary, there are C(14,6)*C(8,8) or 3003 different bit strings that can be formed using six 1s and eight 0s.
  • #1
meatspin
5
0

Homework Statement


How many different bit strings can be formed using six 1s and eight 0s?



Homework Equations



C(n,r) = n!/(r!*(n-r)!)



The Attempt at a Solution



since there's six 1s and eight 0s there are 14 slots. So I'm guessing for the possible six 1s it would be C(14,6) and the remaining eight 0s would have to be C(8,8) since there are only 8 slots left after six 1s are chosen so it would be C(14,6)*C(8,8)?

The last part C(8,8) seems kind of werid so I'm not very convinced this is correct. Any help is apperciated thanks.
 
Physics news on Phys.org
  • #2
Yeah, that's right. The factor of C(8,8), which equals 1, is correct, but usually you just gloss over that since you know the rest of the slots have to be filled with what's left.
 

Related to Solving 6 1s and 8 0s Bit Strings

1. What is a bit string?

A bit string is a sequence of 0s and 1s that represents data in computer systems. Each 0 or 1 is called a bit, and they are used to store and transmit information in digital devices.

2. How many possible combinations are there in a 6 1s and 8 0s bit string?

There are 14 possible combinations in a 6 1s and 8 0s bit string. This can be calculated by using the binomial coefficient formula, nCr = n! / r!(n-r)!, where n is the total number of bits and r is the number of 1s. In this case, n=14 and r=6, resulting in 14! / 6!(14-6)! = 14! / 6!8! = 3003 / 720 = 14.

3. How can you solve a 6 1s and 8 0s bit string?

One possible way to solve a 6 1s and 8 0s bit string is by using a binary decision tree. This involves starting from the leftmost bit and making a decision based on the value of the bit. For example, if the first bit is 0, then we know that the remaining 13 bits must contain 6 1s and 7 0s. This process is repeated until all 14 bits have been assigned a value.

4. What is the significance of 6 1s and 8 0s in a bit string?

The significance of 6 1s and 8 0s in a bit string depends on the context in which it is being used. In some cases, it may represent a specific data pattern or code, while in others it may simply be a random combination of bits with no particular significance.

5. How is a 6 1s and 8 0s bit string related to computer science?

A 6 1s and 8 0s bit string is related to computer science as it is a fundamental concept in digital data representation and storage. It is used in various computer systems and algorithms to store and transmit information, making it an essential component of computer science.

Similar threads

Combination Problem: 8 0s & 10 1s in Bit Strings
    • Calculus and Beyond Homework Help
Replies
2
Views
908
How many number of IP addresses are available?
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
Help me understand this question -- "Three consecutive zeros" in a binary string
    • Engineering and Comp Sci Homework Help
Replies
3
Views
1K
Counting problem - how many ways....
    • Calculus and Beyond Homework Help
Replies
4
Views
3K
Show that the helium ion is bound
    • Advanced Physics Homework Help
Replies
1
Views
1K
Proof by Induction of shortest suffix of concatenated string
    • Calculus and Beyond Homework Help
Replies
1
Views
986
Combinatorics -- Counting Sets of Binary Strings
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
Combinatorics - counting problem
    • Calculus and Beyond Homework Help
Replies
1
Views
3K
Ross chapter 7 The game of clue
    • Calculus and Beyond Homework Help
Replies
3
Views
3K
[Pumping Lemma] About the cases for y in the xy^iz criterion
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top