Number of ways of selecting k objects, no two consecutive
May 10, 2020 · To avoid any of these k k objects being consecutive we also have the additional constraint that there is at least one object in each of the k−1 k 1 buckets between one bar and the …
Generate arbitrarily long sequences of consecutive numbers without ...
Aug 25, 2022 · Question Can those hidden consecutive points have a prime coordinate? If true, then this idea isn't valid. If false (hurray!), is it possible to simplify the Theorem to focus on generating …
The product of $n$ consecutive integers is divisible by $n$ factorial
How can we prove that the product of n n consecutive integers is divisible by n n factorial? Note: In this subsequent question and the comments here the OP has clarified that he seeks a proof that "does …
Expected Number of Coin Tosses to Get Five Consecutive Heads
A fair coin is tossed repeatedly until 5 consecutive heads occurs. What is the expected number of coin tosses?
How do I prove that for every positive integer
I need help proving that for every positive integer n n, there exist n n consecutive positive integers, each of which is composite. The hint that came with the problem is: Consider the numbers
Counting bit strings of length 10 contain either 5 consecutive 0's or 5 ...
Jan 24, 2015 · How many bit strings of length 10 contain either five consecutive 0's or five consecutive 1's ? My Solution: for 5 consecutive 0's After we have filled 0's from $1^{st}$ position we have 2 …
probability - What is the expected number of times a dice has to be ...
The framework proposed in the solution can be generalized to obtain a formula of expected time as of t = 0 t = 0 for n n consecutive throws of any number in the dice as follows.
Proving any product of four consecutive integers is one less than a ...
8 This question already has answers here: Prove that the product of four consecutive positive integers plus one is a perfect square (16 answers)
Why are the differences between consecutive squares equal to the ...
Then you get 9 which is the next cosecutive square, (3^2). That is the concept of the equation above, technically i didn`t explain that specific aspect of the difference of consecutive squares, but i did …
Probability of selecting consecutive floors in an elevator
Jun 29, 2015 · Three people get into an empty elevator at the first floor of a building that has 10 floors. Each presses the button for their desired floor (unless one of the others has already pressed the …