Question

Department of Science and Technology wants to form a committee of three people from a panel of 7 people, out of which 3 are scientists, 3 are bureaucrat and one is both scientist as well bureaucrat. In how many ways can the committee be formed if it should have at least one scientist and one bureaucrat?

• A. 21
• B. 25
• C. 23
• D. 33

Answer 1

The correct option is D 33

$\begin{array}{cc}CASE& \text{No. of ways}\\ \text{2 SCIENTISTS, 1 BUREAUCRAT}& {}^3{C}_2{\times }^3{C}_1=3\times 3=9\\ \text{1 SCIENTIST, 2 BUREAUCRAT}& {}^3{C}_1{\times }^3{C}_2=3\times 3=9\\ \text{2 OUT OF 6 (3 SCIENTIST, 3 BUREAUCRAT),}& {}^6{C}_2\times 1=151\\ WHOISBOTH& \end{array}$

So, total number of ways = 9 + 9 + 15 = 33. Hence option (e)