Question

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

(a). 196
(b). 280
(c). 346
(d). 140

Answer 1

To calculate the number of choices available to the student, we need to consider two scenarios: when the student chooses exactly 4 questions from the first five, and when the student chooses more than 4 questions from the first five. The correct answer is (c) 346.

Step-by-step explanation:

To calculate the number of choices available to the student, we need to consider two scenarios: when the student chooses exactly 4 questions from the first five, and when the student chooses more than 4 questions from the first five.

Scenario 1: Choose exactly 4 questions from the first five. There are 5 choose 4 ways to do this, which is equal to 5. For the remaining 6 questions out of the total 10, the student can choose any 6 from the remaining 8, which is equal to 8 choose 6. So, the number of choices in this scenario is 5 * 8 choose 6.

Scenario 2: Choose more than 4 questions from the first five. There are 5 choose 5 ways to choose all 5 questions from the first five. For the remaining 5 questions out of the total 10, the student can choose any 5 from the remaining 8, which is equal to 8 choose 5. So, the number of choices in this scenario is 5 choose 5 * 8 choose 5.

Now we can calculate the total number of choices by adding the choices from both scenarios: 5 * 8 choose 6 + 5 choose 5 * 8 choose 5 = 280 + 56 = 336.

Therefore, the correct answer is (c) 346.