MAT Exam 2021 Paper

Concept:Use combinations to count selections; divide into cases according to the number chosen from the first five questions.Explanation:The student must choose 10 out of 13 questions.He must choose at least 4 from the first five questions.So there are two possible cases.Case I: Choose 4 from the first five questions and 6 from the remaining 8 questions.Number of ways $= \binom{5}{4} \times \binom{8}{6} = 5 \times 28 = 140$.Case II: Choose all 5 from the first five questions and 5 from the remaining 8 questions.Number of ways $= \binom{5}{5} \times \binom{8}{5} = 1 \times 56 = 56$.Total number of choices $= 140 + 56 = 196$.Answer:The number of choices available is $196$, so the correct option is C.