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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 (2,3,4,5,6,7,8), how many (5)-digit numbers can be formed without repetition and divisible by (4)?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA word is to be formed using (4) distinct consonants and (2) distinct vowels. Letters are chosen from (8) consonants and (5) vowels, then the (6) chosen letters are arranged in any order. How many words are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsFrom (7) students, a president, secretary, and treasurer are to be chosen. No student can hold more than one post. In how many ways can this be done?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsHow many (4)-digit numbers can be formed from digits (1,2,3,4,5,6,7) without repetition such that (4) always appears to the left of (2)?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA signal is made by placing (3) flags one above another. The flags are chosen from (7) distinct flags without repetition. How many signals are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsThere are (4) routes from (P) to (Q) and (5) routes from (Q) to (R). A person goes from (P) to (R) and returns to (P), but must not use the same (P) to (Q) route and the same (Q) to (R) route on return. How many ways are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsUsing all letters of the word (MATRIX), how many arrangements are possible in which the vowels are not together?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsThere are (5) men and (4) women in a meeting. A committee of (5) members is to be formed with exactly (3) men. In how many ways can it be formed?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsUsing digits (0,1,2,3,4,5,6), how many (4)-digit numbers can be formed without repetition and divisible by (3)?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsFrom (6) mathematics books and (5) physics books, a group of (4) books is to be selected with at least one book from each subject. How many groups are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA student must attempt (5) questions out of (8). At least (2) of the first (3) questions must be attempted. In how many ways can the selection be made?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsAn admission code has first (2) distinct letters followed by (3) distinct digits. If letters are chosen from (A,B,C,D,E) and digits from (1,2,3,4,5,6), how many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsUsing the digits (0,1,2,3,4,5), how many (5)-digit numbers can be formed without repetition and divisible by (5)?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsUsing the digits (1,2,3,4,5), how many (4)-digit numbers can be formed without repetition and divisible by (2)?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsOn a website, a main category, subcategory, article, and language are selected. Among (8) main categories, (6) have (5) subcategories and (2) have (3) subcategories; every subcategory has (4) articles and (2) languages. How many page paths are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsIn a (6)-digit OTP, digits may repeat and the first digit cannot be (0). The last two digits are equal, and that digit does not appear in the first four places. How many such OTPs are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA student chooses one class each from 5 morning, 4 afternoon, and 6 evening classes. With the 2 live morning classes, the 3 recorded evening classes cannot be chosen. How many timetables are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA word-style code has the order vowel-consonant-vowel-consonant. There are (5) vowels and (21) consonants, vowels cannot repeat and consonants cannot repeat. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA (5)-character badge has the first (2) places as digits and the next (3) places from (8) letters. The digit sum is even, digits are distinct, and the letters contain (X) exactly once. How many badges are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA four-stage machine sequence has (3,4,5,6) choices respectively. After one machine in the second stage, (2) machines in the third stage cannot be chosen. How many valid sequences are possible?Class 11Permutations and CombinationsFundamental principle of countingHard