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In how many ways a cricketer can score runs with fours and sixes only?

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Important Questions on Permutations and Combinations
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A dice is rolled six times. One, two, three, four, five and six appears on consecutive throws of dices. How many ways are possible of having before ?

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The number of permutations of the letters such that neither the pattern nor occurs is:

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In how many ways can the letters of the English alphabet be arranged so that there are seven letters between the letters and ?

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In an examination, the maximum marks for each of the three papers is each. The maximum marks for the fourth paper is . Find the number of ways with which a student can score marks in aggregate.

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How many rectangles can be formed out of a chess board?

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On a board having rows and columns, find the number of squares.

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On a board having rows and columns, find the number of rectangles.

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How many natural numbers are there that are smaller than and whose decimal notation consists only of the digits and , which are not repeated in any of these numbers?
