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Counting Principle

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

MathematicsWhich formula counts the ways to distribute n distinct objects among r distinct boxes, with each object placed in exactly one box and boxes allowed to be empty?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 (3)-digit numbers are formed from (5) digits with repetition allowed and one digit is (0), what is the count when the first digit cannot be zero?Class 11Permutations and CombinationsDerivations of formulas and their connectionsMedium MathematicsIf repetition is allowed what is the number of ways to fill (3) positions using (4) digits?Class 11Permutations and CombinationsDerivations of formulas and their connectionsEasy MathematicsWhy is nCᵣ taken as 0 when r > n?Class 11Permutations and CombinationsDerivations of formulas and their connectionsEasy MathematicsFrom (10) equally spaced points on a circle, (3) points are to be chosen so that no two chosen points are adjacent. How many selections are possible?Class 11Permutations and CombinationsCombinationsExpert MathematicsFrom (10) teachers and (12) students a group of (7) people is to be formed with at least (3) teachers. How many ways are there?Class 11Permutations and CombinationsCombinationsHard MathematicsIf a set has \(n\) elements, which expression gives the number of its subsets containing at least one element?Class 11Permutations and CombinationsCombinationsMedium MathematicsA school has to form a debate team of 3 students from 8 students. Two particular students cannot be on the same team. Which expression correctly gives the number of such teams?Class 11Permutations and CombinationsCombinationsMedium MathematicsFrom (4) red, (5) blue, and (6) green balls, how many ways are there to choose (1) ball of each color?Class 11Permutations and CombinationsCombinationsMedium MathematicsA committee has 8 members. Two distinct posts, chairperson and secretary, are to be filled. If no member can hold both posts, in how many ways can the chairperson and secretary be chosen?Class 11Permutations and CombinationsCombinationsEasy MathematicsHow many (3)-digit even numbers can be formed from (0,1,3,4,6,8) without repetition?Class 11Permutations and CombinationsPermutationsMedium MathematicsIn how many ways can first, second and third performance order be chosen from (9) singers?Class 11Permutations and CombinationsPermutationsEasy MathematicsHow many ways are there to arrange (4) badges from (10) different badges in order?Class 11Permutations and CombinationsPermutationsEasy MathematicsHow many ways are there to arrange (3) mobile covers from (6) different mobile covers on a shop shelf in order?Class 11Permutations and CombinationsPermutationsEasy MathematicsIn a delivery code, the first (3) positions contain distinct letters chosen from (8) available letters and the last (3) positions contain digits from (0) to (9). If exactly one (0) must appear in the last (3) digits, how many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn a sports tournament, gold, silver, and bronze medal winners are to be chosen from (6) players. If player (A) must not receive any medal, how many outcomes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (5)-digit code is formed using (1,2,3,4). Each digit must appear at least once. How many such codes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA photo-filter app has (5) frames, (6) effects, and (4) text styles. If (2) premium effects are available with only (2) text styles and the remaining effects are available with all (4) text styles, how many combinations are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA password has (3) lowercase letters and (1) special symbol in this order. Lowercase letters may repeat, and the special symbol is chosen from (4) options. If the first letter cannot be a vowel, how many passwords are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert