A complete n-ary tree is one in which every node has 0 or n sons. If x is the…

Let x be the number of internal nodes and L be the number of leaves. The total number of nodes is x + L. Since every internal node has n children, the total number of edges is nx. In a tree, edges equal nodes minus one, so nx = (x + L) - 1. Solving for L yields L = x(n-1) + 1.

Let:

• x = number of internal nodes

• L = number of leaves

• In a complete n-ary tree, every internal node has exactly n children.

Step 1: Total nodes

Total nodes= x+L

Step 2: Total edges

A tree with N nodes has N−1 edges, so:

edges=(x+L)−1

But each internal node contributes exactly n edges, so:

edges=nx

Equate both:

nx=x+L−1

Solve for L:

L=nx−x+1

L=x(n−1)+1

✅ Correct Answer: A. x(n−1)+1