Question

In how many ways can you divide $12$ persons into two groups of three people each and 3 groups of two people each?

• A. $1663200$
• B. $4862200$
• C. $2796330$
• D. $5681030$

Answer 1

The correct option is A $1663200$

Total people $=12,$ they are to be divided into $5$ groups containing $2,2,2,3,3$ people respectively.

$\Rightarrow$ Lets select first $2$ people from $12={}^{12}{C}_2$

$\Rightarrow$ Now, $2$ more from remaining $10={}^{10}{C}_2$ and so on......

$\Rightarrow$ Total $={}^{12}{C}_2\times {}^{10}{C}_2\times {}^8{C}_2\times {}^6{C}_3\times {}^3{C}_3$

$=66\times 45\times 28\times 20\times 1$

$=1663200.$

Hence, the answer is $1663200.$