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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 (4)-letter code is formed from (X,Y,Z,W). No two consecutive letters can be same, and the first and last letters must be same. How many codes can be formed?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA quiz has (8) multiple-choice questions and each has (4) options. A student must choose option (A) in exactly (3) questions. In how many ways can the answer sheet be filled?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA team jersey needs (2) stripe colors and (1) logo color. (7) colors are available. The two stripe colors are different and the logo color is different from both stripe colors. How many designs are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (4)-digit number is to be formed using digits (1) to (9). Digits cannot repeat and the number must start with a digit greater than (5). How many numbers can be formed?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (5)-letter string is formed from (A,B,C,D). Each letter must appear at least once. How many such strings are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (3)-stage security system has (4) choices in the first stage, (5) in the second, and (6) in the third. But if option (A) is chosen in the first stage, only (2) choices remain in the third stage. How many secure paths are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA vehicle number has (2) distinct letters and (4) digits. Digits may repeat, but at least one of the first (2) digits must be (5). How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA student must choose (1) question from each of (4) chapters. The chapters have (5,6,7,8) questions respectively. If the chosen question from the second chapter must not be difficult and it has (2) difficult questions, how many selections are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA safe code has (2) letters and (3) digits. Letters cannot repeat and the sum of the digits must be even. There are (26) choices for letters. How many such codes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsAn identification number has (6) digits. The first (3) digits must be distinct and the last (3) digits may repeat. The first digit is not (0). How many identification numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn an online form, a user chooses (1) of (2) optional languages, (1) of (4) themes, and (2) of (3) security questions with order. How many selections are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsFor class representatives, (4) boys and (5) girls are available. A president and a secretary are to be chosen, and the two posts must go to different persons. If the president must be a girl, in how many ways can it be done?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA book code has (3) distinct consonants and (2) distinct digits. The first symbol is a consonant and the last symbol is a digit. Assume English has (21) consonants. How many codes can be formed?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn a contest, a participant writes true or false for each of (5) questions. At least (1) answer must be true. How many answer patterns are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA mobile lock has (4) distinct digits. The first digit cannot be (0) and the last digit must be even. How many locks can be formed?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA student makes a (6)-day study plan. Each day he studies one subject from Mathematics, Physics, or Chemistry, but he never studies the same subject on consecutive days. How many plans are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsAn exam code has (2) uppercase letters, (1) lowercase letter, and (2) digits in this order. Uppercase letters must be distinct, the lowercase letter has no restriction, and digits may repeat. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA restaurant has (3) types of bread, (5) vegetables, and (4) desserts. A customer chooses either one full plate or only one dessert. How many choices are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA website PIN has (5) digits. The first digit cannot be zero and exactly (2) positions must contain even digits. How many such PINs are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA password has (4) letters and (2) digits. Letters may repeat, but the two digits are distinct and the first digit is not (0). How many passwords are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert