Permutations and Combinations · Class 11 · CBSE · Science Mathematics

From 8 students, a captain and a vice-captain are to be chosen for a team. Explain whether this is a permutation or a combination and find the number…

Practice question from Permutations and Combinations (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

medium · Subjective · Q-3BE30E

From 8 students, a captain and a vice-captain are to be chosen for a team. Explain whether this is a permutation or a combination and find the number of possible selections.

Answer: This is a permutation because the two positions are different, so the order of selection matters. The number of possible selections is 8P2=8×7=56{}^{8}P_{2}=8\times7=56.

Solution

A captain and a vice-captain have distinct roles, so choosing A as captain and B as vice-captain differs from choosing B as captain and A as vice-captain. Therefore, use permutations: 8P2=56{}^{8}P_{2}=56.

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