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?
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?

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

Here 2 courses are compulsory out of 9 courses, so a student need to select

    \[5\text{ }-\text{ }2\text{ }=\text{ }3\text{ }courses\]

∴ Number of ways in which 3 ways can be selected from

    \[9\text{ }-\text{ }2\left( compulsory\text{ }courses \right)\text{ }=\text{ }7\]

are

    \[\Rightarrow {{~}^{7}}{{C}_{3}}=\]

NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Image 37

∴ Number of ways a student selects 5 courses from 9 courses where 2 specific courses are compulsory are: 35