In how many ways 5 students from a group of 10 students be selected if Ankit & Rahul are not selected together

(Q). In how many ways 5 students from a group of 10 students be selected if Ankit & Rahul are not selected together?
Solution:-

number of ways to select 5 student from a group of 10 students without any restriction = ¹⁰C₅ ways
& when both Ankit & Rahul are selected then number of ways to select 5 student is = ⁸C₃
Hence required number of ways = ¹⁰C₅ – ⁸C₃ Answer