Question

If CAT 2009 contains 150 questions and each question contains 5 options, find the total number of ways in which a student can answer atleast two out of 150 questions.

• A. 5¹⁵⁰ -601
• B. 6¹⁵⁰-751
• C. 4¹⁵⁰-601
• D. 6¹⁵⁰-601
• E. none of these

Answer 1

The correct option is B 6¹⁵⁰-751

Option (b)

As a student may answer a question or he may not, So let’s verify the total chances that he can take with a question, i.e. He can take 6 chances with a question namely A,B,C,D,E or not answering it. So with every question he can take 6 chances. So total number of chances is $6^{150}$

From this, we have to deduct these chances: - Total number of ways of answering zero questions as well as one question exactly, which is 1 + (150 $\times$ 5) = 751. So answer is $6^{150}$ – 751.