Linked Questions

1
vote
0answers
51 views

I roll a die $N$ times, what is the probability that the sum is exactly $k$? [duplicate]

The die is six-sided. So, this is easy with a two-sided coin showing exactly $k$ heads, as that is just a Bernoulli trial being run $n$ times (Binomial RV). You can also approximate this using a ...
28
votes
11answers
17k views

What is the probability of the sum of four dice being 22?

Question Four fair six-sided dice are rolled. The probability that the sum of the results being $22$ is $$\frac{X}{1296}.$$ What is the value of $X$? My Approach I simplified it to the equation of ...
14
votes
6answers
2k views

Book on combinatorial identities

Do you know any good book that deals extensively with identities obtained using combinatorial and/or probabilistic arguments (e.g., by solving the same combinatorial or probability problem in two ...
7
votes
5answers
3k views

Probability event with $70$% success rate occurs three consecutive times for sample size $n$

It has been a long time since I've done probability so I am not sure which to do (if either are correct). Thank you for taking the time to look at my work. Probability an event occurs is $70$%. I'm ...
4
votes
6answers
4k views

Number of occurrences of k consecutive 1's in a binary string of length n (containing only 1's and 0's)

Say a sequence $\{X_1, X_2,\ldots ,X_n\}$ is given, where $X_p$ is either one or zero ($0 < p < n$). How can I determine the number of strings, which do contain at least one occurrence of ...
4
votes
3answers
6k views

Efficient algorithm to find all unique combinations of set given duplicates

The number of combinations for a 4 choose 2 is 6. But what if I have a set in which 2 of the elements are the same? Of course I could do a unique check for each item but this is too computationally ...
5
votes
4answers
461 views

Number of q-ary strings of length m which do not contain k consecutive zeros

A finite q-ary-alphabet is given $$A_q = {0,1,2,...,q-1}.$$ Now I am considering the set of all finite strings over the alphabet $A_q$. I am interested on the number $$N(m,k)_{A_q}$$ of strings of ...
6
votes
3answers
741 views

Number of solutions of $x_1 + x_2 + x_3 + x_4 = 14$ such that $x_i \le 6$

Let $x_1, x_2, x_3, x_4$ be nonnegative integers. (a) Find the number of solutions to the following equation: $$ x_1 + x_2 + x_3 + x_4 = 14 $$ I got $17 \choose 3$ for this. Is ...
2
votes
2answers
1k views

Number of solutions of $x_1+x_2+\dots+x_k=n$ with $x_i\le r$

Let $n,k,r$ be positive integers. The number of all nonnegative solutions of the Diophantine Equation $x_1+x_2+\dots+x_k=n$ is $\binom{n+k-1}{n}$. Is there a general formula for the number of ...
7
votes
3answers
737 views

Number of combinations with sets of identical items

I was trying to write a python program which takes a string and prints out all possible combinations of characters from it and in turn figure out the number of such possible combinations of a string ...
3
votes
6answers
314 views

Number of bit strings of length $n$ with no $k_1+1$ consecutive 0s and no $k_2+1$ consecutive 1s.

Just as the question asks. I am trying to calculate the number of bit strings of length $n$ with a maximum of $k_1$ consecutive $0s$ and $k_2$ consecutive 1s. Of course we assume $k_1+k_2\leq n$. I am ...
1
vote
2answers
4k views

How to calculate dice roll probability with more dice? [duplicate]

I'm no math graduate, so be patient. For two dice it is easy, because of the small number of possibilities, and it’s still easy for three, but how can I work out the case for ten (with some formula)? ...
4
votes
2answers
3k views

How do you calculate the sum of combinations of 1000 dice rolls?

For two dice rolls we can calculate the number of combinations for each summed total: Rolling a 2: one chance (1&1) Rolling a 3: two chances (2&1)(1&2) Rolling a 4: three chances (3&1)...
2
votes
2answers
538 views

Probability of rolling a sum of at least 18 with 10 6-sided dice

I'm trying to work out how to do this, and I'm very stuck. My grasp of probability is shaky to begin with, and generally with probability questions, I list out cases. Due to the number of ...
3
votes
2answers
1k views

Probability to obtain more than X with 3 dice.

This is a dice problem 1) I want to calculate the probability to have more than X throwing 3 dice of 6 faces. X = addition of the result of the 3 dice. 2) This is the first step but if you can also ...

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