Question

in an examination paper on business mathematics, there are 14 questions divided into three groups of 5, 5 and 4 questions respectively. a candidate is required to answer 6 questions taking at least two questions from each of the first two groups and atleast one question from the third group. in how many different ways can he make up his choice?

Answer 1

The candidate can make their choice in 2,704 different ways.

Step-by-step explanation:

To calculate the number of different ways the candidate can choose their questions, we need to consider the requirements stated in the question. The candidate needs to answer at least two questions from the first two groups and at least one question from the third group.

For the first group, the candidate can choose 2, 3, 4, or 5 questions out of the 5 available. This can be done in C(5,2) + C(5,3) + C(5,4) + C(5,5) = 10 + 10 + 5 + 1 = 26 ways.

Similarly, for the second group, the candidate can choose 2, 3, 4, or 5 questions out of the 5 available. This can be done in C(5,2) + C(5,3) + C(5,4) + C(5,5) = 10 + 10 + 5 + 1 = 26 ways.

For the third group, the candidate needs to choose 1 question out of the 4 available. This can be done in C(4,1) = 4 ways.

The total number of different ways the candidate can make their choice is obtained by multiplying the number of choices from each group: 26 × 26 × 4 = 2,704 ways.