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JEE Main Mathematics question

MathematicsPermutations and CombinationsJEE Main

A man has friends. If is number of ways he can invite one friend everyday for dinner on successive nights so that no friend is invited more than times then the value of is

Answer: 3

Solution

Sequences of nights with friends: ; we remove sequences where some friend is invited at least times. For one given friend the counts give

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Question ID VK-020717