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Mathematics : Permutations and Combinations

Short Answer Type

11. A cinema hall has 3 entrance and 4 exit gates. In how many ways can he enter the hall and leave it at the end of the show?

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12. A room has 4 doors. In how many ways can a child enter the room and leave by a different door?

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13. Find the number of 4 letter words with or without meaning which can be formed out of the letters of the word ROSE, where the repetition of the letters is not allowed.

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14.

How many:

(a) 2-digit even numbers (b) 3-digit even numbers

can be formed using the digits 1, 2, 3, 4, 5 when repetition of digits is not allowed?

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15. How many 4-letter code can be formed using the first 10 letters of the English alphabet, repetition of letters is (a) allowed (b) not allowed?

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16. A class has 20 students. Prizes for standing first, second and third in Mathematics are to be awarded. In how many ways can this be done?

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17. A class has 30 students. First prizes in Physics, Chemistry and Mathematics are to be awarded. In how many ways can this be done?

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18.

Find the number of 3-digit numbers when

(a) repetition of digit is allowed. (b) repetition of digits is not allowed.

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19. How many 4-digit numbers greater than 7000 can be formed by using the digits 3, 5, 7, 8, 9, if repetition is not allowed?

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20. In how many ways 5 rings of different types be worn in 4 fingers when there is no restriction on the number of rings in each finger?

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