Here we need 2 equations ,
a) No of edges = No of vertices - 1 [ Basic definition of tree ]
b) Handshaking theorem i.e. sum of degree = 2 * no of edges
Say no of leaf nodes = x
Hence sum of degree due to leaf nodes = x
Now for non root nodes , degree = 4 as 1 due to parent and 3 due to 3-ary ness of tree..
For root node , degree = 3..
Hence ,
Sum of degree = 2 * no of edges
==> 3 + 9 * 4 + x = 2 * ( x + 10 - 1 ) [ As no of edges = no of vertices - 1 and no of vertices = x + 10 ]
==> 39 + x = 2x + 18
==> x = 21
Hence no of leaf nodes = 21