Question

7. A student was given 15 questions in a test. Find the number of choices if:

a) He must answer 10 questions only.

b) He must answer 10 questions but the first 5 are compulsory.

c) He must answer 10 questions, where the first 5 from Section A question 1 to 8, and another 5 from Section b, question 9 to 15.

d) He must answer 10 questions, where at least 6 question from Section A question 1 to 8.

Answer 1

a)

Number of ways of selecting 10 questions out of 15 is

b)

Since first five are compulsory so we need to select 5 questions out of rest 10 questions so the required number of ways is

c)

Number of ways of selecting 5 from section A consists of 8 questions and number of ways of selecting other 5 from section B consisting of 7 questions is

d)

That is we need to select 6, 7 or 8 question from section A and remaing from section B. The required number of ways is