Question

Number of ways in which $10$ different things can be divided into two groups containing $6$ and $4$ things respectively is ?

Answer 1

Forming the first group by choosing 4 things out of 10 things,the total number of ways will be $={}^{10}{C}_4$

Now,forming these group by choosing 6 things,the total number of ways $={}^6{C}_6$

Therefore,the total number of ways $={}^{10}{C}_4\ast {}^6{C}_6$

$\frac{(10\ast 9\ast 8\ast 7)}{(4\ast 3\ast 2\ast 1)}\ast \frac{(6\ast 5\ast 4\ast 3\ast 2\ast 1)}{(6\ast 5\ast 4\ast 3\ast 2\ast 1)}$

$\frac{72}{2}\ast \frac{210}{6}\ast 1$

$210\ast 1=210$ ways