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Class 11MathematicsPermutations and CombinationsCombinationsExpert
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To go from one point to another, (7) right moves and (4) up moves are required. How many shortest paths are possible?

Answer and explanation

Correct answer: 330

A shortest path has 11 moves in total: 7 right moves and 4 up moves. Each path is determined by choosing the 7 positions for the right moves among these 11 positions. Therefore, the number of paths is \(\binom{11}{7}=\binom{11}{4}=330\). The value \(252=\binom{10}{5}\), so it does not apply here. Exam tip: In grid-path questions, choose the positions of one type of move among all moves.

Related tags

Permutations And CombinationsCombinationsGrid PathsShortest PathsBinomial CoefficientMathematicsClass 11 Mcq
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