(Q). There are 10 singers who is ready to perform in a show that is scheduled for two timings, before lunch & after lunch. If before lunch maximum 6 singers can perform while after lunch maximum 5 singers can perform then in how many different way program can be scheduled?
Solution:-
Here two cases will be formed:-
case(i).
Before lunch 6 & after lunch 5 then number of ways is ¹⁰C₆ = 210 ways (∵ we just have to select only 6 out of 10 before lunch remaining 4 will be automatically selected in 1 way)
Case(ii).
After lunch 5 then before lunch it should be 5 singers & that can be done in ¹⁰C₅ ways = 252 ways
Hence total number of ways is = 210 + 252
= 462 Answer