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Three variables have a sum of . All three of them are non-negative integers. If any two variables don't have the same value and exactly one variable has a value of less than or equal to three, then find the number of possible solutions for the variables.
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Important Questions on Permutations and Combinations
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The letters of the word ALLAHABAD are rearranged to form a new word and put in a dictionary. If the dictionary had only these words and one word on every page in alphabetical order then what is the page number on which the letter LABADALAH comes?
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If and can only take the values then find the number of solutions of the equation .
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There are nine points in a plane such that no three are collinear. Find the number of triangles that can be formed using these points as vertices.
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There are nine points in a plane such that exactly three points out of them are collinear. Find the number of triangles that can be formed using these points as vertices.
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If is a two-digit number and are the digits, then find the number of solution of the equation .
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Ten points are marked on a straight-line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?
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For a scholarship, at the most candidates out of can be selected. If the number of different ways of selection of at least one candidate is , what is the maximum number of candidates that can be selected for the scholarship?
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One red flag, three white flags and two blue flags are arranged in a line such that:
(a) no two adjacent flags are of the same colour
(b) the flags at the ends of the line are of different colours.
In how many different ways can the flags be arranged?
