# Q.9.     In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

9 courses are available and 2 specific courses are compulsory for every student.

Therefore, every student has to select 3 courses out of the remaining 7 courses.

This can be selected in $^7C_3$ ways.

Thus, using multiplication priciple, number of ways of selecting courses  $=^7C_3$

$=\frac{7!}{3!4!}$

$= \frac{7\times 6\times 5}{ 3\times 2}$

$=35$

Exams
Articles
Questions
The passage contains a mathematical question about selecting courses and provides a detailed solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Q.9.     In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

9 courses are available and 2 specific courses are compulsory for every student.

Therefore, every student has to select 3 courses out of the remaining 7 courses.

This can be selected in $^7C_3$ ways.

Thus, using multiplication priciple, number of ways of selecting courses  $=^7C_3$

$=\frac{7!}{3!4!}$

$= \frac{7\times 6\times 5}{ 3\times 2}$

$=35$

Exams
Articles
Questions
user
The passage contains a mathematical question about selecting courses and provides a detailed solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER