What is the probability of being dealt 4 hearts from a standard 52-card deck if only 4 cards are to be dealt?

To determine the probability of being dealt 4 hearts from a standard 52-card deck when only 4 cards are drawn, we first need to calculate the total number of outcomes and the number of favorable outcomes.

In a standard deck, there are 13 hearts. When we are looking to draw 4 cards, we can think of the scenario in terms of combinations (which is used to calculate the number of ways to choose items from a larger set). The total number of ways to choose 4 cards from the 52-card deck can be calculated using the combination formula:

[ \text{Total combinations of 4 cards from 52} = \binom{52}{4} ]

Next, we consider the favorable outcomes, which is the number of ways to choose all 4 cards from the 13 hearts:

[ \text{Favorable combinations of 4 hearts from 13} = \binom{13}{4} ]

The probability of an event can be computed as the ratio of the number of favorable outcomes to the total number of outcomes:

[ P(\text{4 hearts}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{\binom{