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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।

MathematicsA password has (6) positions. Exactly (3) letters and (3) digits are used from (5) letters and (5) digits without repetition. The first and last positions cannot both be digits. How many passwords are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn a grid, one moves from ((0,0)) to ((5,4)) using only right and up moves. The path must not pass through either ((2,2)) or ((4,3)). How many paths are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsUsing digits (1,2,3,4,5,6,7,8,9), how many (5)-digit numbers can be formed without repetition and divisible by (9)?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsHow many binary strings of length (10) have exactly (4) ones, no two ones adjacent, and the first position equal to (0)?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsFrom (8) men and (7) women, a committee of (6) members is to be formed. The committee must have at most (3) women. How many committees are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsHow many distinct arrangements of the letters of (STATISTICS) are possible if no two vowels are adjacent?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsUsing the digits (0,1,2,3,4,5,6,7), how many (5)-digit even numbers can be formed without repetition and with the digit (3) included?Class 11Permutations and CombinationsFundamental principle of countingExpert Mathematics(6) speakers are to speak in order on a stage. Of two particular speakers, one must be in the first three positions and the other must be in the last three positions. How many speaking orders are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA question paper has (5) questions in section (A) and (6) questions in section (B). A student must attempt (6) questions with at least (2) from section (A) and at least (3) from section (B). In how many ways can the selection be made?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsUsing digits (0,1,2,3,4,5,6,7), how many (3)-digit numbers can be formed without repetition such that the hundreds digit is greater than the units digit?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsAmong (9) people, (3) are friends. A committee of (5) is to be formed with exactly (2) of these (3) friends included. How many committees are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA game has (5) distinct red and (4) distinct blue cards. A sequence of (4) cards is to be made such that the first and last cards have different colours. How many sequences are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA password has (5) distinct letters. They are to be arranged so that exactly (2) letters lie between two particular letters. How many arrangements are possible?Class 11Permutations and CombinationsFundamental principle of countingHard Mathematics(3) questions are to be selected from (6) questions, but question (1) and question (2) cannot be selected together. How many selections are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA shop has (4) types of pens and (3) types of notebooks. A student buys (2) distinct pens and (2) distinct notebooks. How many selections are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA (6)-digit number is formed using all digits (0,1,2,3,4,5). How many such numbers have (0) and (5) not together?Class 11Permutations and CombinationsFundamental principle of countingHard Mathematics(8) distinct objects are to be placed in (3) empty positions, with at most one object in each position. How many ways are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsFrom (5) teachers and (6) students, a group of (4) persons is to be formed with at least (1) teacher and at least (2) students. How many groups are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsUsing digits (1,2,3,4,5,6), how many (4)-digit numbers can be formed without repetition and greater than (3000)?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsAmong (10) points, no (3) are collinear. How many triangles can be formed if (2) particular points must not appear together in any triangle?Class 11Permutations and CombinationsFundamental principle of countingHard