Four cards are drawn from a full pack of cards . Find the probability that
there is one card of each suit,

Answer

To find the probability that there is one card of each suit when drawing four cards from a full pack of cards, we can follow these steps:

### Step 1: Understand the total number of cards and suits
A standard deck of cards has 52 cards, divided into 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards.

### Step 2: Calculate the total number of ways to draw 4 cards from 52
The total number of ways to choose 4 cards from a deck of 52 cards can be calculated using the combination formula:

\[ \text{Total ways} = \binom{52}{4} \]

Calculating this gives:

\[ \binom{52}{4} = \frac{52!}{4!(52-4)!} = \frac{52 \times 51 \times 50 \times 49}{4 \times 3 \times 2 \times 1} = 270725 \]

### Step 3: Calculate the number of favorable outcomes
To have one card from each suit, we need to select one card from each of the four suits. The number of ways to choose one card from each suit (hearts, diamonds, clubs, and spades) is:

\[ \text{Favorable outcomes} = 13 \times 13 \times 13 \times 13 = 13^4 \]

Calculating this gives:

\[ 13^4 = 28561 \]

### Step 4: Calculate the probability
The probability of drawing one card from each suit is the ratio of the number of favorable outcomes to the total number of outcomes:

\[ P(\text{one card from each suit}) = \frac{\text{Favorable outcomes}}{\text{Total ways}} = \frac{13^4}{\binom{52}{4}} = \frac{28561}{270725} \]

### Step 5: Simplify the probability
To simplify this fraction, we can calculate:

\[ P(\text{one card from each suit}) \approx 0.1055 \]

Thus, the probability that there is one card of each suit when drawing four cards from a full pack of cards is approximately 0.1055.

### Summary
The probability that there is one card of each suit when drawing four cards from a full pack of cards is:

\[ P = \frac{28561}{270725} \approx 0.1055 \]