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Fundamental Principle Of Counting

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

MathematicsUsing digits (0,1,2,3,4,5,6,7,8), how many (5)-digit numbers can be formed without repetition if only odd digits occupy odd positions?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematics(8) persons are to be seated around a circle. Between two particular persons, there must be exactly (2) persons in one direction. How many arrangements are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsIn a grid, one moves from ((0,0)) to ((5,5)) using only right and up moves. The path must pass through exactly one of ((2,3)) and ((4,4)). How many paths are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsUsing digits (0,1,2,3,4,5,6,7,8,9), how many (6)-digit numbers can be formed without repetition, divisible by (25), and containing the digit (7)?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematics(8) distinct tasks are to be distributed among (3) persons (A,B,C). Person (A) must get exactly (3) tasks and person (B) must get at least (2) tasks. How many distributions are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsUsing (4) vowels and (6) consonants, how many strings of (6) letters can be formed if repetition is allowed, exactly (2) vowels are used, and no two vowels are adjacent?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematics(9) distinct books are to be placed on (3) labeled shelves. Each shelf must contain at least one book, and the order of books on each shelf matters. How many ways are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematics(4) integers are to be selected from (1) to (12). No two selected integers should be consecutive, and their sum must be even. How many selections are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematics(5) boys and (4) girls are to be seated in (9) positions in a row. Girls can sit only in odd-numbered positions. How many arrangements are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsA registration number has first (2) distinct letters followed by (4) digits. Letters are chosen from (6) available letters. In the digits, exactly one pair must be equal and the other two digits must be different from it and from each other. How many registration numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsFrom (7) players, ordered gold, silver, and bronze positions are chosen. Then an unordered practice pair is selected from the remaining players. How many ways are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsHow many distinct arrangements of the letters of (BANANA) are possible if no two (A)'s are adjacent?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsFrom (5) mathematics, (4) physics, and (3) chemistry books, (6) books are to be selected. The selection must contain books from exactly (2) subjects. How many selections are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsUsing digits (0,1,2,3,4,5,6,7,8,9), how many (8)-digit numbers can be formed without repetition if both (0) and (5) occur, but neither is at an end?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsAmong (12) points, (5) points are collinear, and no other (3) points are collinear. How many quadrilaterals can be formed?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsHow many solutions does (x_1+x_2+x_3+x_4=12) have if (x_1 \ge 2), (x_2) is positive odd, (0 \le x_3 \le 4), and (x_4 \ge 0)?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematics(8) persons are to be seated around a circle. Two particular persons must sit together, but a third particular person must not sit next to either of them. How many arrangements are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematicsA box has (6) red, (5) blue, and (4) green balls. (5) balls are to be selected with all three colours present and more red balls than green balls. How many selections are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematics(4) boys and (3) girls are to be seated in a row. All girls must sit together, and two particular boys must not sit together. How many arrangements are possible?Class 11Permutations and CombinationsFundamental principle of countingExpertMathematics(5) distinct prizes are to be distributed among (3) students. Each student must receive at least one prize. How many ways are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert

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