A group of 9 students, s ₁, ~s ₂, , s ₉ , is to be divided to from three teams X , Y , and Z of sizes 2,3 , and 4 , respectively. Suppose that s₁ cannot be selected for the team X , and s ₂ cannot be selected for the team Y. Then the number of ways to from such teams, is

Step-by-step solution

array ccc x & y & z 2 & 3 & 4 array C-i) when x does not contain S ₁ , but contains S ₂ ( (for x) ^7 C₁ (for y,z) 7! 3!4! =245 ) C-ii) When x does not contain S ₁, ~S ₂ and y does not contain S ₂ i.e. ( (for x) ⁷ C ₂ (for y,z) 6! 3!3! =420 ) so total No. of ways 665