ISRO 2014- probability [EE]

Question

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
(A) 140
(B) 196

(C) 280

(D) 346

Comments

(5C4 * 8C6) + (5C5 * 8C5) = 196

Answer 1

There are two possibilities,

Case 1: 4 out of 5 starting questions are answered then 6 out of remaining 8 questions. Possible number of ways is 

⁵C₄ × ⁸C₆ = 140

Case 2: 5 out of 5 starting are answered and then 5 out of remaining 8. Possible number of ways is

⁵C₅ × ⁸C₅ = 56

So total number of ways is 140+56 = 196(option B)

Answer 2

196 is right.