A) 200
B) 300
C) 500
D) 350
Correct Answer: B
Solution :
| Number of different teams consisting of 2 girls (out of 5) and 3 boys (out of 7)\[=\,({}^{5}{{C}_{2}}\times {{\,}^{7}}{{C}_{2}})\]out of these. |
| Number of teams consisting of 2 specific boys A and B \[=\,({}^{5}{{C}_{2}}\times {{\,}^{2}}{{C}_{2}}\times {}^{5}{{C}_{1}})\] |
| Answer \[=\,({}^{5}{{C}_{2}}\times {{\,}^{7}}{{C}_{3}})\,-({}^{5}{{C}_{2}}\times {}^{5}{{C}_{1}})\]\[=\,{}^{5}{{C}_{2}}\times {{(}^{7}}{{C}_{3}}-{}^{5}{{C}_{1}})\]\[=10\times \,(35-5)\,=\,300\] |
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