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:

The student needs to choose 10 questions total. The constraint is to pick at least 4 from the first 5.There are two possible cases:Choosing exactly 4 from the first 5 questions:Number of ways = ${}^5{C}_4\times {}^{13-5}{C}_{10-4}={}^5{C}_4\times {}^8{C}_6=5\times 28=140$.Choosing exactly 5 from the first 5 questions:Number of ways = ${}^5{C}_5\times {}^{13-5}{C}_{10-5}={}^5{C}_5\times {}^8{C}_5=1\times 56=56$.Total choices = $140+56=196$.