91Ó°ÊÓ

Total no. of people in the group (n) =100

People selected from the group at random (r) = 12

The possibility of selecting 12 people from a group of 100 people =\(^{100}{C_{12}}\)

The possibility that both A and Bwill be selected=\(^2{C_2}\)

Therefore, the probability that both A and B will be selected is be given by,

\(\begin{aligned}{}{\rm{P}} &= \frac{{\left( {^2{C_2}{ \times ^{98}}{C_{10}}} \right)}}{{^{100}{C_{12}}}}\\ &= \left( {\frac{{1 \times \frac{{98!}}{{\left\{ {10!\left( {98 - 10} \right)!} \right\}}}}}{{\frac{{100!}}{{\left\{ {12!\left( {100 - 12} \right)!} \right\}}}}}} \right)\\ &= \frac{{\frac{{98!}}{{880!}}}}{{\frac{{100!}}{{1056!}}}}\\ &= 0.01333\end{aligned}\)

Thus, the required probability is 0.01333.