(Q). In class (V) there are three sections A, B & C with number of students 50, 70 and 90 respectively while in class (vi) there are three sections A, B & C with number of students 70, 90 & 50 respectively. In how many ways 15 students can be selected either from class V or class VI equal from section A, B & C.
Solution:-
Equal number of students means 5 students from each section.
case(i).
If student are selected from class V then number of ways is ⁵⁰C₅×⁷⁰C₅×⁹⁰C₅
case(ii).
If students are selected from class VI then the number of ways is ⁷⁰C₅×⁹⁰C₅×⁵⁰C₅
∴ Total number of ways = either case(i) OR case(ii)
= ⁵⁰C₅×⁷⁰C₅×⁹⁰C₅ + ⁷⁰C₅×⁹⁰C₅×⁵⁰C₅ Answer