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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 (6)-letter word is formed using (A,B,C). Each letter must appear at least once. How many such words are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn an app, a user must pass through (3) security levels. The levels have (2,4,5) choices respectively. If choosing a special option at the second level reduces the third level by (2) choices, how many paths are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (4)-digit code can use only odd digits (1,3,5,7,9). Digits may repeat, but the code cannot start with (5). How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsOn a box, (2) symbols and (2) colors are printed in order. (6) symbols and (5) colors are available. The two symbols must be distinct and the two colors must be distinct. How many print designs are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (3)-digit number is to be formed using digits from (1) to (7). Digits may repeat and the number must be greater than (400). How many numbers can be formed?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn an exam of (6) questions with (5) options each, a student answers every question. The same option cannot be chosen in any two consecutive questions. How many answer patterns are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA travel plan visits 3 cities A, B and C. For each city, 2 hotels and 3 local transport options are available. If the order of cities is fixed, how many plans are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsOn a library shelf, one Mathematics book and one Science book must be placed in order from (5) Mathematics and (4) Science books. If the first place is for Mathematics and the second for Science, how many arrangements are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (7)-digit number is formed from (0,1,2,\ldots,9). Digits may repeat, the first digit is not (0), and the last (2) digits are same. How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert 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 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