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 s_1 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
A. A
array ccc x & y & z \\ 2 & 3 & 4 array C-i) when x does not contain S _1, but contains S _2 \( (for x) ^7 C_1 (for y,z) 7! 3!4! =245\) 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
Related: Mathematics — Permutation Combination · All PYQ Banks