Question

the number of ways in which 9 things can be divided into twice groups containing 2,3 and 4 things respectively is ?

Answer 1

Here , total number of things = 9,
So forming the first group by choosing 2 things out of 9 things that is, = ⁹C₂
Now next group is formed by choosing 3 things out of 7 remaining things, that is, = ⁷C₃
And next group is formed by choosing 4 things out of remaining 4 things, = ⁴C₄
Hence the number of ways = ⁹C_{2 $\times$} ⁷C_3$\times$ ⁴C₄ = 1260.