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There are ten boys B_{1}, B_{2}, \ldots, B_{10} and five girls G_{1}, G_{2}, \ldots, G_{5} in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B_{1}$ and $B_{2}  together should not be the members of a group, is_____________.

Option: 1

1120


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{n(B)=10 ,\quad n(a)=5}

The number of ways of forming a group of 3 girls of 3 boys

\mathrm{={ }^{10} C_{3} \times{ }^{5} C_{3}} \\

\mathrm{=\frac{10 \times 9 \times 8}{3 \times 2} \times \frac{5 \times 4}{2}=1200}

The number of ways whe two particular boys \mathrm{B_{1}\: and\: B_{2}} be the member of group together

\mathrm{=^8{C_{1}} \times^{5 } {C_{3}}=8 \times 10=80}

Number of ways boys \mathrm{B_{1}\: and\: B_{2}} are not in the same group together

Required no.of selections  =  \mathrm{1200-80=1120}

Hence answer is \mathrm{1120}

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