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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।

MathematicsA code is formed by writing (2) distinct vowels followed by (3) distinct digits. If digits are from (0) to (9), how many codes can be formed?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA four-letter code is formed from (P,Q,R,S,T). Repetition is not allowed and (P) and (Q) must not be adjacent. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA vehicle number has two distinct letters followed by four digits. Digits may repeat, but all four digits cannot be identical. How many vehicle numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingHard MathematicsA 6-place code has 3 choices for each of the first 2 places, 4 choices for each of the next 2 places, and 2 choices for each of the last 2 places. The two places in the middle pair must have different choices; repetition is allowed elsewhere. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA school trip plan includes choosing 1 of 5 buses, 1 of 4 meal packs, and 1 of 3 museum options. A guide is optional, and there are 2 guides available. How many plans are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA café offers 7 drinks, 5 snacks, and 3 desserts. A customer may choose only a drink, a drink with a snack, or a complete set consisting of a drink, a snack, and a dessert. How many options are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA code consists of 3 distinct digits followed by 2 distinct letters. The available digits are 0, 1, 2, 3, 4, 5, and 6, and the available letters are P, Q, R, S, and T. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA digital certificate can have 5 title styles, 4 seals, 3 borders, 2 signature colors, and 2 languages. How many designs are possible if one choice is made in each category?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsUsing the digits 0, 1, 2, 3, 4, 5, 6, and 7 without repetition, 4-digit numbers are formed. The first digit cannot be 0, and the last digit must be a non-zero even digit. How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA 4-question test has 3, 4, 5, and 2 options for its questions, respectively. One answer must be selected for each question. How many answer patterns are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsIn a competition, first, second, and third prizes are awarded among 9 participants. No participant can receive more than one prize. How many outcomes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA 5-place PIN is formed using the digits 0, 1, 2, 3, 4, and 5. The first two places must contain different digits, and the last digit must differ from the first. Repetition is allowed in all other places. How many PINs are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsAn 8-letter set includes M and N. A 3-letter code uses each letter at most once, and its first letter is fixed as M. The last letter cannot be N. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA 4-digit number is formed with its first two digits chosen from 1, 2, 3, 4 and its last two digits chosen from 5, 6, 7, 8, 9. Repetition is not allowed within either pair. How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA 4-place signal is formed as follows: the first place is chosen from 5 colors, the second and third places use different shapes chosen from 6 shapes, and the fourth place is chosen from 4 icons. How many signals are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA shopkeeper has 6 packet types and 8 label types. Four specific packet-label pairs are not allowed. Each allowed pair is available in 3 sizes. How many valid options are there?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsUsing the digits 1–9, form 4-digit numbers without repeating any digit. The number must be greater than 6000. How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsAn exam portal lets a user choose from 6 classes, 5 subjects, 4 test types, 3 modes, and 2 time slots. How many test options are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA 5-letter code has vowels in its first 3 places and consonants in its last 2 places. There are 5 available vowels and 7 available consonants, with no letter repeated. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA photo app offers 6 filters, 5 frames, and 4 stickers. A sticker is optional, and at most one sticker can be used. How many different photo looks are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium