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Question
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
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Solution
From 4 officers and 8 jawans, 6 need to be chosen. Out of them, 1 is an officer.
Required number of ways =\[{}^4 C_1 \times {}^8 C_5 = 4 \times \frac{8!}{5! 3!} = 4 \times \frac{8 \times 7 \times 6 \times 5!}{5! \times 6} = 224\]
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