Question
Mathematics Question on Combinations
A student is asked to answer 10 out of 13 questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is
A
186
B
176
C
286
D
196
Answer
196
Explanation
Solution
The correct option is (D) 196.
(i) Choosing 4 out of the first five questions and 6 out of the remaining 8 questions. Therefore, the number of choices in this case is given by 5 C 4×8 C 6=5 C 1×8 C 2=5×8×1×27=140.
(ii) Choosing 5 out of the first five questions and 5 out of the remaining 8 questions. This leads to 5 C 5×8 C 5=1×8 C 3=5×8×1×2×37=56.
Hence, the total number of choices is 140+56=196140+56=196.