Maths-
General
Easy
Question
If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr –1 + 2 × nCr equals-
- n + 1Cr +1
- n+2Cr
- n+2Cr+1
- n+1Cr
Hint:
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Here we have given nCr denotes the number of combinations of n things taken r at a time, we have to find the expression nCr+1 + nCr –1 + 2 × nCr.
The correct answer is: n+2Cr+1
A permutation is the non-replaceable selection of r items from a set of n items in which the order is important.

A combination is created by selecting r items from a group of n items without replacing them and without regard to their order.

Here we have given: nCr denotes the number of combinations of n things taken r at a time, so

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .
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