Final answer:
A combinatorial proof for the identity k * (n choose k) = n * (n-1 choose k-1) can be understood by considering the ways to choose a team of k members with a leader from n individuals, highlighting that both sides of the equation represent the same counting problem.
Step-by-step explanation:
The student is asking for a combinatorial proof for the identity k * (n choose k) = n * (n-1 choose k-1) where 0 ≤ k ≤ n. This identity can be proven by interpreting the terms combinatorially. Consider a group of n individuals, and we want to select a team of k members with a leader. The left-hand side, k * (n choose k), represents choosing a team of k members from n people first, and then choosing one of these k members to be the leader. The right-hand side, n * (n-1 choose k-1), represents choosing the leader first from the n individuals, and then choosing the remaining k - 1 members from the remaining n - 1 individuals. Both procedures will result in a team of k with one leader, hence they count the same scenario and prove the equality.