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From 4 Officers and 8 Jawans in How Many Ways Can 6 Be Chosen. to Include at Least One Officer? - Mathematics

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From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?

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Solution

 From 4 officers and 8 jawans, 6 need to be chosen and at least one of them is an officer.
Required number of ways =  Total number of ways -  Number of ways in which no officer is selected

\[=^{12} C_6 -^8 C_6 \]
\[ = \frac{12!}{6! 6!} - \frac{8!}{6! 2!} \]
\[ = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7}{6 \times 5 \times 4 \times 3 \times 2 \times 1} - \frac{8 \times 7}{2} \]
\[ = 924 - 28\]
\[ = 896\]

Concept: Combination
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 9.2 | Page 16

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