A scientific committee is to be formed from 6 | vedclass

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(A) Let $I$ be the number of Indians and $F$ be the number of foreigners. We are given $I \ge 2$ and $F = 2I$.Since there are $6$ Indians and $8$ fore

Vedclass · Accepted Answer

$1625$

Vedclass · Answer

(A) Let $I$ be the number of Indians and $F$ be the number of foreigners. We are given $I \ge 2$ and $F = 2I$.Since there are $6$ Indians and $8$ foreigners available,we must satisfy $I \le 6$ and $F \le 8$.Substituting $F = 2I$,we get $2I \le 8$,which implies $I \le 4$.Thus,the possible values for $I$ are $2, 3, 4$.$I$ (Indians)$F$ (Foreigners)Number of ways$2$$4$${}^{6}C_{2} 	imes {}^{8}C_{4} = 15 	imes 70 = 1050$$3$$6$${}^{6}C_{3} 	imes {}^{8}C_{6} = 20 	imes 28 = 560$$4$$8$${}^{6}C_{4} 	imes {}^{8}C_{8} = 15 	imes 1 = 15$Total number of ways $= 1050 + 560 + 15 = 1625$.

$A$ 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

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