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Permutations And Combinations

Class 11 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsWhich identity explains why C(n+r−1, r) equals C(n+r−1, n−1)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhat is the number of ways to distribute n identical balls among r distinct boxes if every box must be nonempty?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhat is the number of ways to distribute n identical balls among r distinct boxes if empty boxes are allowed?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhich relation is most useful for identifying the largest binomial coefficient C(n, r) as r varies?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf C(n, r−1):C(n, r) = 3:5, which expression for the ratio is useful in deriving a relation between n and r?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhat counting argument gives C(n, r) = (n/r)C(n−1, r−1), for 1 ≤ r ≤ n?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsThe identity C(m+n, r) = Σ[k=0 to r] C(m, k)C(n, r−k) is proved by which counting split?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhich combinatorial idea explains the identity \(\sum_{r=0}^{n}\binom{n}{r}=2^n\)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhy is the coefficient of x^r in (1+x)^n equal to \(\binom{n}{r}\)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf at least (1) object must be selected from (n) objects, why are the total selections (2^n-1)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsAmong (7) distinct points no (3) are collinear. Why is the number of triangles given by (^{7}C_3)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf (8) people are arranged in a row but (2) special people must stay together, the block method is based on which formula connection?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsA (4)-person committee is to be formed from (6) men and (5) women with exactly (2) women. Which formula is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf (3) students are to be chosen from (5) boys and (4) girls with at least (1) girl, what is the shortest formula derivation route?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhy are (r) and (n-r) interchangeable in (^{n}C_r) but not in (^{n}P_r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf (^{n}P_r=^{n}P_{n-r}) is not true for every (r), what is the main reason?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWriting (^{20}C_3) as (\frac{20\cdot19\cdot18}{3!}) comes from which cancellation?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhy is the formula for (^{18}C_2) (\frac{18\cdot17}{2}), and how is it connected to (\frac{18\cdot17}{2!})?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf (^{n}C_r=\frac{^{n}C_{r-1}(n-r+1)}{r}), what kind of derivation is this?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIn a repeated-letter word like (MISSISSIPPI), division by (4!4!2!) comes from which principle?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard