I have read in high school the logical meaning of this formula. The value of C (n, k) can be recursively calculated using following standard formula for Binomial Coefficients. I remember my teacher saying that to calculate number of ways of selecting r objects from n objects(nCr) , we can either discard object at r postion(i.e n-1Cr-1) , or we can include the object at r position (i.e n-1Cr).but I don’t understand this logic now …!! Then, for each student there are two possibilities that either it would be selected in that group of r students or it will be rejected.

@va1ts7_100 It can be understood as, suppose you want to select a group of r students out of N students, which can be done in \binom{N}{r} ways. A binomial coefficient C (n, k) can be defined as the coefficient of X^k in the expansion of (1 + X)^n. If you select A in the group then you have total N-1 students left and you have to select remaining r-1 students, which can be done in \binom{N-1}{r-1} ways, and if you don’t select ’A’ then you have total N-1 students left and you have to select r students from it which can be done in \binom{N-1}{r}. Powered by Discourse, best viewed with JavaScript enabled, Need some explanation on the combinatorics formula nCr= n-1Cr + n-1Cr-1. The formula follows from considering the set {1, 2, 3,..., n} and counting separately (a) the k-element groupings that include a particular set element, say "i", in every group (since "i" is already chosen to fill one spot in every group, we need only choose k − 1 from the remaining n − 1) and (b) all the k-groupings that don't include "i"; this enumerates all the possible k-combinations of nelements. Really, wonderful explanation. Thank you very much, bro. C (n, k) = C (n-1, k-1) + C (n-1, k) C (n, 0) = C (n, n) = 1 Following is a simple recursive implementation that simply follows the recursive structure mentioned above. Combination is the selection of data from the given in a without the concern of arrangement. I have read in high school the logical meaning of this formula.

A k-combination with repetitions, or k-multicombination, or multisubset of size k from a set S is given by a sequence of k not necessarily distinct elements of S, where order is not taken into account: two sequences define the same multiset if one can be obtained from the other by permuting the terms.In other words, the number of ways to sample k elements from a set of n elements allowing for … can someone plz explain me this with some example or any editorial…?? A binomial coefficient C (n, k) also gives the number of ways, disregarding order, that k objects can be chosen from among n objects; more formally, the number of k-element subsets (or k-combinations) of an n-element set. Thank you. nCr= n-1Cr + n-1Cr-1 is a famous recursive equation for computing nCr , where nCr means number of ways selecting r objects from n objects.

nCr= n-1Cr + n-1Cr-1 is a famous recursive equation for computing nCr, where nCr means number of ways selecting r objects from n objects. Let, out of these N students there is a student ’A’ which will either be selected in group of those r students or won’t be selected. Given with n C r, where C represents combination, n represents total numbers and r represents selection from the set, the task is to calculate the value of nCr. So, the total number of ways of selecting r students out of N students is equal to \binom{N-1}{r} + \binom{N-1}{r-1}.

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