If 10 identical coins are distributed among 4 children at random. The probability of distributing so that each child gets atleast one coin is

10 identical coins are distributed among 4 children at random

$$\begin{gathered} n=10,r=4 \\ n\left(S\right)={ }^{n+r-1}{C}_{r-1}={ }^{13}{C}_3 \end{gathered}$$

E= Event  of distributing so that each child gets atleast one coin 

$n\left(E\right)={ }^{n-1}{C}_{r-1}={ }^9{C}_3$

$P\left(E\right)=\frac{{ }^9{C}_3}{{ }^{13}{C}_3}=\frac{9\times 8\times 7}{13\times 12\times 11}=\frac{42}{143}$