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From 4 Officers and 8 Jawans in How Many Ways Can 6 Be Chosen (I) to Include Exactly One Officer - Mathematics

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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 =\[{}^4 C_1 \times {}^8 C_5 = 4 \times \frac{8!}{5! 3!} = 4 \times \frac{8 \times 7 \times 6 \times 5!}{5! \times 6} = 224\]

Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 9.1 | Page 16

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