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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।

MathematicsAn exam roll number has (2) letters followed by (3) digits. The first letter must be a vowel, the second a consonant, and the (3) digits must not repeat. Assume (5) vowels in the English alphabet. How many roll numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (5)-letter signal uses only (A,B,C,D,E,F). The first and last letters must be different, but the middle (3) letters may repeat. How many signals are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn a building with (8) doors, different doors are chosen for entry and exit. A third door, different from both, is chosen for emergency exit. Order matters. How many ways are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (3)-stage process has (4) choices at the first stage. If the first selected choice is a special one, the second stage has (5) choices, otherwise each of the remaining (3) first choices gives (2) choices. The third stage always has (6) choices. How many outcomes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsHow many (4)-digit numbers with distinct digits can be formed such that exactly (2) digits are from (2,4,6,8) and the remaining digits are from (1,3,5,7,9)?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA quiz has (5) multiple-choice questions. The first (2) questions have (4) options each and the remaining (3) questions have (5) options each. If every question must be answered, how many answer patterns are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsAn email prefix is made of (3) lowercase letters and (2) digits. Letters do not repeat and digits do not repeat. The first position is a letter and the order is letter, letter, letter, digit, digit. How many prefixes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsUsing digits from (1) to (9), how many (3)-digit numbers can be formed that are odd and have no repeated digit?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA vehicle number has (2) letters followed by (4) digits. The letters must be different, digits may repeat, and the first digit cannot be (0). How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsFrom (7) students a class representative, an assistant representative, and a sports representative are to be chosen. No student can hold more than one post. How many selections are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA mobile PIN has (4) digits. The first digit cannot be (0), the last digit must be even, and the two middle digits may be any digits. Repetition is allowed. How many PINs are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA menu has (4) soups, (5) main dishes, and (3) desserts. A customer may take soup with main dish, main dish with dessert, or all three. How many meal choices are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA secure locker code has (5) symbols. The first symbol is chosen from (4) special signs, the last from (3) colors, and the middle (3) symbols from (8) digits without repetition. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsUsing (0,1,2,3,4,5), how many (4)-digit numbers divisible by (5) can be formed without repetition of digits?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA paper has three sections. Choose one question from two in the first section, two questions from four in order in the second section, and one question from three in the third section. How many answer sequences are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsFrom (5) different cities a trip needs a starting city and an ending city. They must be different and (2) different intermediate stops are also chosen from the remaining cities. If order matters then how many trips are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA website password must have (4) letters followed by (3) digits. Letters are chosen from the English alphabet without repetition and digits from (0) to (9) with repetition allowed. How many passwords are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (6)-digit code is formed where the first (2) places can contain only odd digits and the remaining (4) places can contain only even digits. If no digit is repeated then how many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsFrom (9) students, a debate team of (4) is to be formed, and (2) speakers are to be chosen in order from that team. One particular student must be in the team but must not be a speaker. How many ways are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert Mathematics(8) distinct books are to be arranged in a row. Two particular books must be together, and a third particular book must be at one end of the row. How many arrangements are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert