Who was the first to prove the binomial theorem?
The theorem can be generalized to include complex exponents for n, and this was first proved by Niels Henrik Abel in the early 19th century.
Where does n choose k come from?
(pronounced “n choose k” ) is the number of distinct subsets of size k of a set of size n. More informally, it’s the number of different ways you can choose k things from a collection of n of them (hence n choose k).
How is binomial expansion used in real life?
Real-world use of Binomial Theorem: The binomial theorem is used heavily in Statistical and Probability Analyses. It is so much useful as our economy depends on Statistical and Probability Analyses. In higher mathematics and calculation, the Binomial Theorem is used in finding roots of equations in higher powers.
What does the binomial formula tell us?
The Binomial theorem tells us how to expand expressions of the form (a+b)ⁿ, for example, (x+y)⁷. The larger the power is, the harder it is to expand expressions like this directly. But with the Binomial theorem, the process is relatively fast!
Who discovered binomial distribution?
mathematician Jakob Bernoulli
Swiss mathematician Jakob Bernoulli, in a proof published posthumously in 1713, determined that the probability of k such outcomes in n repetitions is equal to the kth term (where k starts with 0) in the expansion of the binomial expression (p + q)n, where q = 1 − p. (Hence the name binomial distribution.)
Who Discovered expansion in mathematics?
In 1670, James Gregory gave the formula for the binomial expansion of a fractional power. Newton wanted to find the areas under the curves of the above formula or equations. [1] Coolidge, J.L. “The Story Of The Binomial Theorem”.
What is n choose k equal to?
N choose K is called so because there is (n/k) number of ways to choose k elements, irrespective of their order from a set of n elements. To calculate the number of happenings of an event, N chooses K tool is used. This is also called the binomial coefficient. The formula for N choose K is given as: C(n, k)= n!/[k!(
What does 5 choose 3 mean?
5C3 or 5 choose 3 refers to how many combinations are possible from 5 items, taken 3 at a time. What is a combination? Just the number of ways you can choose items from a list.
Why is binomial expansion important?
The binomial theorem gives us the general formula for the expansion of (a+b)n for any positive integer n. It also enables us to determine the coefficient of any particular term of an expansion of (a+b)n.
Why is binomial theorem useful?
The theorem and its generalizations can be used to prove results and solve problems in combinatorics, algebra, calculus, and many other areas of mathematics. The binomial theorem also helps explore probability in an organized way: A friend says that she will flip a coin 5 times.
What is n in statistics?
Population Mean The symbol ‘N’ represents the total number of individuals or cases in the population.
Who invented Poisson distribution?
mathematician Siméon-Denis Poisson
The French mathematician Siméon-Denis Poisson developed his function in 1830 to describe the number of times a gambler would win a rarely won game of chance in a large number of tries.
Why is binomial called binomial?
The algebraic expression which contains only two terms is called binomial. It is a two-term polynomial. Also, it is called a sum or difference between two or more monomials.
What is the value of 10 C 3?
10c3 = 10 x 9 x 8/3!
What is 5c2 worth?
In both of our solving processes, we see that 5 C 2 = 10. In other words, there are 10 possible combinations of 2 objects chosen from 5 objects.
How was the binomial theorem discovered?
According to our current understanding, the Binomial Theorem can be traced to the 4- th century B.C. and Euclid where one finds the formula for (a + b)2. In the 3-rd century B.C. the Indian mathematician Pingala presented what is now known as “Pascal’s triangle” giving binomial coefficients in a triangle.