# A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes atleast 2 Indian and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is : Option: 1 1050 Option: 2 575 Option: 3 1625 Option: 4 560

$\begin{array}{l} (2 \mathrm{I}, 4 \mathrm{~F})+(3 \mathrm{I}, 6 \mathrm{~F})+(4 \mathrm{I}, 8 \mathrm{~F}) \\ ={ }^{6} \mathrm{C}_{2}{ }^{8} \mathrm{C}_{4}+{ }^{6} \mathrm{C}_{3}{ }^{8} \mathrm{C}_{6}+{ }^{6} \mathrm{C}_{4}{ }^{8} \mathrm{C}_{8} \\ =15 \times 70+20 \times 28+15 \times 1 \\ =1050+560+15=1625 \end{array}$

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