Verified Solution • 2025–26 Session moderate QJEEM25Ma5e96: JEE Main 2025 Mathematics - Class 11 JEEM25Ma5e96 Solution: Group A consists of 7 boys and 3 girls, while group B consists… Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group AAA and the remaining 3 from group BBB , is equal to : Multiple Choice Options A 8925 B 9100 C 8575 D 8750 Step-by-Step Verified Solution C-I amp;(3G&2 B)&(1G&2 B) C-II amp;(2G&3 B)&(2G&1 B) C-III amp;(1G&4 B)&(3G&0 B)\begin{array}{ll}\text { C-I } & (3 \mathrm{G} \& 2 \mathrm{~B}) \&(1 \mathrm{G} \& 2 \mathrm{~B}) \\\text { C-II } & (2 \mathrm{G} \& 3 \mathrm{~B}) \&(2 \mathrm{G} \& 1 \mathrm{~B}) \\\text { C-III } & (1 \mathrm{G} \& 4 \mathrm{~B}) \&(3 \mathrm{G} \& 0 \mathrm{~B})\end{array} C-I C-II C-III amp;(3G&2 B)&(1G&2 B)amp;(2G&3 B)&(2G&1 B)amp;(1G&4 B)&(3G&0 B) amp; Total = C-I + C-II + C-III amp;=7C2⋅3C3⋅6C2⋅5C1+7C3⋅3C2⋅6C15C2+7C4⋅3C1⋅6C0⋅5C3amp;=8925\begin{aligned}& \text { Total }=\text { C-I }+ \text { C-II }+ \text { C-III } \\& ={ }^7 \mathrm{C}_2 \cdot{ }^3 \mathrm{C}_3 \cdot{ }^6 \mathrm{C}_2 \cdot{ }^5 \mathrm{C}_1+{ }^7 \mathrm{C}_3 \cdot{ }^3 \mathrm{C}_2 \cdot{ }^6 \mathrm{C}_1{ }^5 \mathrm{C}_2+{ }^7 \mathrm{C}_4 \cdot{ }^3 \mathrm{C}_1 \cdot{ }^6 \mathrm{C}_0 \cdot{ }^5 \mathrm{C}_3 \\& =8925\end{aligned}amp; Total = C-I + C-II + C-III amp;=7C2⋅3C3⋅6C2⋅5C1+7C3⋅3C2⋅6C15C2+7C4⋅3C1⋅6C0⋅5C3amp;=8925 Related Learning Resources & Exam Preparation JEE Main PYQ Question Bank Browse year-wise authentic previous years' questions with solutions Authentic CBT Mock Tests Simulate official exam environment with live timer and percentile scoring
