Find the probability that when a hand of 7 cards is dealt from a well-shuffled deck of 52 cards, it contains (i) all 4 kings (ii) exactly 3 kings (iii) at least 3 kings.

Explanation

To solve the problem, we will break it down into three parts as specified in the question.

### Part (i): Probability of getting all 4 Kings

1. **Total ways to choose 7 cards from 52**:
We can calculate the total number of ways to choose 7 cards from a deck of 52 cards using the combination formula:
\[
\text{Total ways} = \binom{52}{7}
...