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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।

MathematicsFour different letters are to be placed into five different envelopes. Each letter may go into any envelope, and envelopes may remain empty. How many arrangements are possible?Class 11Permutations and CombinationsFundamental principle of countingEasy MathematicsIn a (6)-digit number, the first (2) digits must be the same and the last (4) digits can be any digits from (0) to (9). The first digit cannot be (0). How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA badge is made by choosing one shape, one colour, and one letter. There are 4 shapes, 3 colours, and 5 letters. If the circular shape allows only 2 colours and each of the other 3 shapes allows all 3 colours, how many badges are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsIn a (5)-position seating code, each position is filled with one of (A,B,C). Consecutive (A)'s are not allowed only in the first two positions. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsFrom (9) players, a captain, a vice-captain, and a wicketkeeper are to be selected. (2) special players cannot be wicketkeeper and no player can hold two positions. How many selections are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA club membership card is made using (2) colors, (5) shapes, and (4) symbols. If the red color allows only (2) symbols while the other color allows all (4) symbols, how many cards are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (3)-digit number is formed from (2,3,4,5,6,7). The number must be less than (400), and digits may repeat. How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn a (4)-letter word signal, letters are chosen from (8) letters. The first and second letters must be different, the third must be the same as the first, and the fourth must not be the same as the second. How many signals are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA student must choose one notebook for each of (3) different subjects. There are (5), (4), and (6) choices for the subjects respectively. The student also chooses (1) pen from (2) pens. How many study kits are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn a (5)-digit secret number, the first digit is from (1) to (9), the second digit must be greater than the first, and the remaining (3) digits may be any digits. Repetition is allowed. How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn (5) empty positions, (2) distinct red balls, (1) blue ball, and (2) blank marks are to be placed. The red balls are counted distinctly and the blue ball is distinct. How many patterns are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsThere are (4) bus routes and (3) rail routes. A traveler either goes by bus and returns by rail, or goes by rail and returns by bus. How many travel options are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn a (6)-key password, the first (3) keys are chosen from (7) letters without repetition and the last (3) keys from (4) symbols with repetition allowed. How many passwords are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsIn a competition among (6) teams, first, second, and third places are to be awarded. The previous winner cannot get first place. No team can receive more than one place. How many outcomes are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (4)-digit number is formed from (0,1,2,3,4,5,6). It must be even, the first digit must not be (0), and no digit is repeated. How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA (5)-letter signal must contain exactly (2) vowels and (3) consonants. Assume (5) vowels and (21) consonants, with no letter repeated. How many signals are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA computer folder name is made from (2) letters and (2) digits. Exactly (1) letter must be uppercase and (1) lowercase, their positions may vary, and the two digits must be different. How many names are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsA row of (6) boxes is to be colored red, blue, or green. The first and last boxes must not have the same color. How many color patterns are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsUsing (1,2,3,4,5,6,7), how many (4)-digit numbers greater than (3000) can be formed without repetition?Class 11Permutations and CombinationsFundamental principle of countingExpert MathematicsAn online form has (4) yes-no questions and (2) questions with (3) options each. If every question must be answered, how many response combinations are possible?Class 11Permutations and CombinationsFundamental principle of countingExpert