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The latest registration number issued by the Delhi Motor Vehicle Registration Authority is DL-5S 2234. If all the numbers and alphabets before this have been used up, then find how many vehicles have a registration number starting with DL-5?

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Important Questions on Permutations and Combinations

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There are 100 balls numbered n1, n2, n3, n4,.....n100. They are arranged in all possible ways. How many arrangements would be there in which n28, ball will always be before n29 ball and the two of them will be adjacent to each other?
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Find the sum of the number of sides and number of diagonals of a hexagon.
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A tea party is arranged for 2M people along two sides of a long table with M chairs on each side. R men wish to sit on one particular side and S on the other. In how many ways can they be seated (provided R, S  M).
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In how many ways can 'mn' things be distributed equally among n groups?
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In how many ways can a selection be made of 5 letters out of 5As, 4Bs, 3Cs, 2Ds and 1Es?
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Find the number of ways of selecting 'n' articles out of 3n+ 1, out of which n are identical.
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The number of positive numbers of not more than 10 digits formed by using 0, 1, 2, 3 is
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There is a number lock with four rings with each ring having digits 0 to 9. How many attempts at the maximum would have to be made before getting the right number?