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Ramesh has 6 friends. In how many ways can he invite one or more of them at a dinner?

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Important Questions on Permutations & Combinations

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From 4 gentlemen and 6 ladies a committee of five is to be selected. Find the number of ways in which the committee can be formed so that gentlemen are in majority.
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8 pens are to be selected from pens of 3 colours (pens of each colour being available any number of times), then find the total number of selections.
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Number of ways of selecting three squares on a chessboard so that all the three be on a diagonal line of the board or parallel to it is

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The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is
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How many different 3-letter words can be formed with the letter of word JAIPUR when A and I are always to be excluded?
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If all the letters of the word QUEUE are arranged in all possible manner as they are in a dictionary, then the rank of the word QUEUE is
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The total number of ways in which 8 men and 6 women can be arranged in a line so that no 2 women are together is