Section A contains 3, section B contains 4,
section C contains 5 questions. Find the
number of ways of selecting 6 questions taking
atleast one from each section

No. of questions in section, A=3, no. of questions
in section B =4, no. of questions in section C=5,
Required no. of attempting 6 questions = total
no. of selections – selections
Expect question from C – selection except from
A – selection except from B
$$\begin{gathered} ={}^{12}C_6-{}^{7}C_6-{}^{9}C_6-{}^{8}C_6 \\ =924-7-84-28=805 \end{gathered}$$