UGC NET Paper 1 GA 2012 Dec Solved Paper

The group must formed by 4, 5 or 6 boys and 3, 2 or 1 girls
the required number of ways when group formed by 4 boys and 3 girls
Number of ways for this selection ${}_{}^6{\mathit{C}}_4^{}{\times }^4{\mathit{C}}_3$
when group formed by 5 boys and 2 girls Number of ways for this selection
${}_{}^6{\mathit{C}}_5^{}{\times }^4{\mathit{C}}_2$
when group formed by 6 boys and 1 girl the number of ways for this selection
${}_{}^6{\mathit{C}}_6^{}{\times }^4{\mathit{C}}_1$
total number of ways $=15\times 4+6\times 6+1\times 4$
$=60+36+4=100.$