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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।

MathematicsIf (n) distinct objects are divided into labelled groups of sizes (a,b,c) and (a+b+c=n), which formula is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsBy changing the order of selection, ({}^{n}C_r{}^{r}C_s{}^{s}C_t) can be correctly written as which form?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the simplified form of (\sum_{r=0}^{n}{}^{n}C_r{}^{r}C_k)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the correct form of (\sum_{r=0}^{n}r^2{}^{n}C_r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the correct simplified form of (\sum_{r=0}^{n}r(r-1){}^{n}C_r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhy does (2^{n-1}) appear on the right side of (\sum_{r=0}^{n}r{}^{n}C_r=n2^{n-1})?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat does (r(r-1)) count in (r(r-1){}^{n}C_r=n(n-1){}^{n-2}C_{r-2})?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the double-counting interpretation of (r{}^{n}C_r=n{}^{n-1}C_{r-1})?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is ({}^{n}C_r\cdot r!(n-r)!) always equal to?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhich idea is most suitable to prove (\sum_{r=0}^{n}{}^{n}C_r^2={}^{2n}C_n)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWhat is the most correct combinatorial basis of the identity (\sum_{k=0}^{r}{}^{m}C_k{}^{n}C_{r-k}={}^{m+n}C_r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsExpert MathematicsWith which factorial form can ({}^{n}C_a{}^{n-a}C_b) be connected?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsThe identity ({}^{m+n}C_r=\sum_{k=0}^{r}{}^{m}C_k{}^{n}C_{r-k}) is a form of which identity?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhat is the simplified form of (\sum_{r=0}^{n}{}^{n}C_r{}^{r}C_2)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhich double counting gives (\sum_{r=0}^{n}r{}^{n}C_r=n2^{n-1})?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhat is the correct selection-based interpretation of the symmetry \,\(^{n}C_r=^{n}C_{n-r}\)\, in combinations?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsHow is (\sum_{r=0}^{n}{}^{n}C_r=2^n) understood through subsets?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhy is the coefficient of (a^{n-r}b^r) in ((a+b)^n) equal to (^{n}C_r)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard Mathematics(5)-character passwords are formed from (7) symbols without repetition. Which count is correct?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard Mathematics(5)-character passwords are formed from (7) symbols with repetition allowed. Why is the count (7^5)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard