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nCr Definitions and Properties

Question

From $4$ officers and $8$ jawans , in how many ways can $6$ be chosen such that to include exactly one officer .

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Solution

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${1.}^{4} C_{1} =$ no of ways $1$ officer can be selected
$^{8} C_{5} =$ no of ways $5$ jawans can be selected
Total no of ways $=^{4} C_{1} \times^{8} C_{5}$

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