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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।

MathematicsUsing the digits 0–9, form 4-digit numbers with repetition allowed. The number must be from 2000 to 5999, inclusive. How many numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA student can choose one shirt from 5 shirts, one pair of trousers from 3 pairs, and one pair of shoes from 2 pairs, or choose one bag from 7 bags instead. How many choices are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA code has 3 letter positions followed by 2 symbol positions. Each letter position has 5 choices, and repetition of letters is allowed. There are 4 symbols available, and symbols cannot repeat. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA 5-digit PIN uses the digits 0 through 8. Its first digit cannot be 0, and its last digit must be even. Repetition is allowed. How many PINs are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA meal consists of one starter chosen from 5, one main dish chosen from 4, and optionally one dessert chosen from 3 and one drink chosen from 2. How many different selections are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsThere are 4 routes from home to a center and 6 routes from the center to a library. On the return trip, the route used on each stage of the outward trip cannot be reused in reverse. How many round trips are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsUsing the letters A, B, C, D, E, F, G, and H, form 3-letter codes without repetition. The first letter cannot be A or B. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA sequence has 6 positions, and 5 colors are available. No two consecutive positions may have the same color. How many sequences are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA password has 3 letter positions followed by 2 digit positions. Each letter position has 4 choices, and each digit position has 6 choices. Repetition is allowed. How many passwords are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA code consists of 2 distinct letters followed by 3 distinct digits. There are 7 letters and 5 digits available. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsHow many 3-digit even numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, and 7 without repetition?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsHow many 4-digit numbers less than 4000 can be formed using the digits 0, 1, 2, 3, 4, 5, and 6 without repetition?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsHow many 4-digit odd numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, and 8 without repetition?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA 5-place code allows 2 choices at each of the first 3 places and 5 choices at each of the last 2 places. Repetition is allowed. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA signal has 4 places, with 3 colors available at each place. The colors in the first and third places must be the same, and repetition is allowed. How many signals are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA code consists of 2 distinct digits followed by 2 distinct letters. The available digits are 0, 1, 2, 3, and 4, and the available letters are P, Q, R, and S. How many codes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA 4-digit number is formed using distinct digits from 0, 1, 2, 3, 4, 5, and 6. Its first digit cannot be 0, and its last digit must be odd. How many such numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsFirst and second prizes are awarded among 8 participants. No participant can receive both prizes. How many outcomes are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA 4-place PIN uses the digits 0, 1, 2, 3, and 4. The digits in the first two places must be different, while repetition is allowed in the remaining places. How many PINs are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium MathematicsA 3-digit number must be greater than 200 and less than 700. Its digits are chosen from 1, 2, 3, 4, 5, 6, 7, and 8 without repetition. How many such numbers are possible?Class 11Permutations and CombinationsFundamental principle of countingMedium