A scientific committee is to formed from $6$ Indians and $8$ foreigners, which includes at least $2$ Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is:

560

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1050

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1625

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575

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Solution

The correct option is C $1625$
The possible ways are
$(2 I, 4 F) + (3 I, 6 F) + (4 I, 8 F)$
$=^{6} C_{2} \cdot^{8} C_{4} +^{6} C_{3} \cdot^{8} C_{6} +^{6} C_{4} \cdot^{8} C_{8}$
$= 15 \times 70 + 20 \times 28 + 15 \times 1$
$= 1050 + 560 + 15 = 1625$

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