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Permutations

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

MathematicsFor integers \(0\le r\le n\), given \({}^{n}P_r=r!\binom{n}{r}\), why is \({}^{n}P_r\ge\binom{n}{r}\)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWriting \(\binom{n}{r}=\frac{n(n-1)\cdots(n-r+1)}{r!}\) shows which connection?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsFor fixed \(n\ge2\) and integers \(0\le r<s\le n-1\), why is \({}^{n}P_s>{}^{n}P_r\)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsFour different prizes are given to 10 students, with no student receiving more than one prize. How many distributions are possible?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIn which case would replacing P(n,r) with n^r give the wrong count?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsFour-digit numbers are formed using six available non-zero digits, with repetition allowed. Why is the count 6^4?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsThere are n distinct objects and r specified, distinct positions to fill, with no object used more than once. Which formula counts the arrangements?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsUnder which condition does the arrangement formula n!/(p!q!) apply?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsArrange 6 boys and 4 girls in a row so that no two girls are together. What is the main step in the derivation?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsArrange 8 people in a row so that A and B are not next to each other. Which expression gives the number of arrangements?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhy is the number of ordered queues of 3 people chosen from 7 equal to C(7,3)×3!?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsFour specified students are to be seated in a row of 10 seats, with the remaining seats empty. Which expression counts the arrangements?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf \(^{12}P_4=^{12}C_4\cdot x\), what is the correct value of (x)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsWhich of the following situations is represented by the expression \(\binom{n}{r}r!\)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIf \(^{n}P_2=^{n}C_2\cdot k\), what is the value of (k)?Class 11Permutations and CombinationsDerivations of formulas and their connectionsHard MathematicsIn the product form of (^{n}P_r), if (r=6), what is the last factor?Class 11Permutations and CombinationsDerivations of formulas and their connectionsMedium MathematicsWhich of the following is the correct relationship between permutations and combinations?Class 11Permutations and CombinationsDerivations of formulas and their connectionsMedium MathematicsIn the product form of (^{n}P_r), if (r=5), what is the last factor?Class 11Permutations and CombinationsDerivations of formulas and their connectionsMedium MathematicsIf ⁿPᵣ = 24 × ⁿCᵣ, what is the value of r?Class 11Permutations and CombinationsDerivations of formulas and their connectionsMedium MathematicsIf ⁿP₂ = 90, what is the value of n using the permutation formula?Class 11Permutations and CombinationsPermutationsMedium