Question

The vice-chancellor of ABC University decided to form a committee to look into the feasibility of introduction of semester systems at the undergraduate level. Five members from the Executive Council and 7 members from the Academic Council were found to be suitable for the job. In how many ways can the vice-chancellor form the committee of 6 members such that at least 4 members of the committee belong to the Academic Council?

• A. 350
• B. 462
• C. 455
• D. 456
• E. 420

Answer 1

Answer: (B)

462

Answer 2

Number of members from Executive Council = 5
Number of members from Academic Council = 7
A committee of 6 members is to be formed such that at least 4 members of the committee should belong to the Academic Council.
So, required number of ways
$={^7}C_4\times {^5}C_2 + {^7}C_5\times {^5}C_1+{^7}C_6$
$=\frac{5\times 6\times 7}{2\times3}\times\frac{4\times5}{2}+\frac{6\times7}{2}\times5+7$
$=350+105+7=462$
So, the correct answer is B.