I need help with this problem. It is about Discrete math- Pigeonhole principle converse.

I know what answers are ; a= 28, and b=229, but I need What P(n), Base step, and inductive step are...

(a)

A team wishes to purchase 10 shirts of the same color. A store sells shirts in 3 different colors. What must the inventory of the store be in order to conclude that there are at least 10 shirts in one of the three colors?

(b)

How many people must be selected to make sure that there are at least 20 who are born in the same month?

All the problems below are about mathematical induction. Identify P (n); that is, what is the general statement you're trying to prove? Then make sure you prove the following: (i) the base step and (ii) the inductive step.

About Mathematical Induction :

Goal: To prove that P (n) is true for every positive integer n.

Steps:

Base step: Show P(1) is true.

Inductive step: Show that P(k)P(k+1) for every positive integer k.

That is, for each such k, assume P(k) is true and then show that P(k + 1) follows from it.

Theorem: The basis and inductive steps imply that P (n) is true for all positive integers n.