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How many different car licence plates ca...

How many different car licence plates can be constructed, if the licences contain three letters of the English alphabet followed by a three digit number, if repetition are allowed?

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To find the total number of different car license plates that can be constructed with the given conditions, we can break the problem down into two parts: the letters and the digits. ### Step 1: Determine the number of choices for the letters The license plate starts with three letters from the English alphabet. Since repetition is allowed, each letter can be any of the 26 letters (A to Z). - For the first letter, there are 26 choices. - For the second letter, there are also 26 choices. - For the third letter, again, there are 26 choices. ...
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Assertion: The number of different number plates which can be made if the number plte contain three letters of the English alphabet followied by athree digit number is (26)^3xx(900) (if represents are allowed) Reason: The number of permutationis of n different things taken r at time when repetitios are allowed is n^r . (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

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ARIHANT MATHS ENGLISH-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. How many different car licence plates can be constructed, if the licen...

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  2. There is a rectangular sheet of dimension (2m-1)xx(2n-1), (where m > 0...

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  3. If the letters of the word SACHIN are arranged in all possible ways...

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  4. lf r, s, t are prime numbers and p, q are the positive integers such t...

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  5. At an election a voter may vote for nany number of candidates , not gr...

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  6. The letters of the word COCHIN are permuted and all the permutation...

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  7. The set S""=""{1,""2,""3,""........ ,""12) is to be partitioned into...

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  8. Consider all possible permutations of the letters of the word ENDEANOE...

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  9. How many different words can be formed by jumbling the letters in the ...

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  10. In a shop, there are five types of ice-creams available. A child buys ...

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  11. The number of seven digit integers, with sum of the digits equal to 10...

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  12. From 6 different novels and 3 different dictionaries, 4 novels and ...

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  13. There are two urns. Urn A has 3 distinct red balls and urn B has 9 ...

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  14. Statement-1: The number of ways of distributing 10 identical balls in ...

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  15. There are 10 points in a plane, out of these 6 are collinear. The numb...

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  16. The total number of ways in which 5 balls of differert colours can be ...

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  17. Let n denote the number of all n-digit positive integers formed by the...

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  18. Let a(n) denote the number of all n-digit numbers formed by the digits...

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  19. Assuming the balls to be identical except for difference in colours, t...

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  20. Let Tn be the number of all possible triangles formed by joining ve...

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  21. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

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