Mathematics - Application of Derivative Question with Solution | TestHub

We know that the number of ways of dividing $(\mathrm{m}+\mathrm{n}+\mathrm{p})$ things into three groups containing $\mathrm{m},\mathrm{n}$ and $\mathrm{p}$ things respectively $$=\frac{(\mathrm{m}+\mathrm{n}+\mathrm{p})!}{\mathrm{m}!\mathrm{n}!\mathrm{p}!}$$ Further if any two groups out of the three have same number of things then number of ways $$=\frac{(m+n+p)!}{m!n!p!\times 2}$$ Hence number of ways to divide 10 students into three teams one containing four students and each remaining two teams contain three $=\frac{10!}{4!3!3!\times 2}=\frac{10\times 9\times 8\times 7\times 6\times 5}{3\times 2\times 3\times 2\times 2}=2100$