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(Q). 8 students has to be selected such that 4 students from science group & 4 students from Arts group. Number of participants in different group is as follows:-
Science group:- Total 9 students – 5boys and 4 girls
Art group:- Total 9 students – 4 boys and 5 girls
How many ways group of 8 students can be selected if it has 4 boys and 4 girls?
Solution:-

Following different cases can be made:-

Science groupArt groupBoysBoysGirlsGirls(5)(5)(4)(4)Case(i)Case(ii)Case(iii)Case(iv)Case(v)01234012344321043210Number of ways⁵C₀×⁴C₄×⁴C₄×⁵C₀ = 1⁵C₁×⁴C₃×⁴C₃×⁵C₁ = 400⁵C₂×⁴C₂×⁴C₂×⁵C₂ = 3600⁵C₃×⁴C₁×⁴C₁×⁵C₃ = 1600⁵C₄×⁴C₀×⁴C₀×⁵C₄ = 25

Hence total number of ways
 = 1 + 400 + 3600 + 1600 + 25
5626 ways         Answer