Cards are drawn one at random from a well shuffled full pack of 52 playing cards until 2 aces are obtained for the first time. If `N` is the number of cards required to the drawn, then show that `P ,{N=n}=((n-1)(52-n)(51-n))/(50xx49xx17xx13),w h e r e2

Explanation

To solve the problem, we need to find the probability \( P(N = n) \) where \( N \) is the number of cards drawn until the second ace is obtained for the first time. We will break down the problem step by step.

### Step 1: Understanding the Problem
We need to draw cards from a deck of 52 until we get 2 aces. The first ace must appear in the first \( n-1 \) draws, and the second ace must appear on the \( n \)-th draw.

### Step 2: Counting the Ways to Draw Cards
1. **First Ace in the First \( n-1 \) Draws**:
We need to choose 1 ace from the 4 available aces and \( n-2 \) non-aces from the remaining 48 cards (since there are 52 cards total, and we have already chosen 1 ace).
...