A scientific committee is to be 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:

Number of Indians = 6

Number of foreigners=8

Number of foreigners in the committee = 2(No. of Indians in the committee).

Total number of committees

       = committees with

$(2I, 4f)+ (3I, 6f)+(4I, 8f)$

$\begin{array}{rcl} & =& 6_{{\mathrm{C}}_2}\times 8_{{\mathrm{C}}_4}+6_{{\mathrm{C}}_3}\times 8_{{\mathrm{C}}_6}+6_{{\mathrm{C}}_4}+8_{{\mathrm{C}}_8}\\ & =& 15\times 70+20\times 28+15\times 1\\ & =& 1050+560+15=1625 \end{array}$