Four cards are drawn at random from a standard playing pack of fifty two cards. Find the probability that the random draw will yield the 4 queens

In this problem, we are asked to find the probability that a random draw of 4 cards from a standard 52-card deck yields exactly the 4 queens.

### Step 1: Total Possible Outcomes
The total number of ways to draw 4 cards from a deck of 52 cards can be calculated using combinations:

\[
\text{Total outcomes} = \binom{52}{4} = \frac{52 \times 51 \times 50 \times 49}{4 \times 3 \times 2 \times 1} = 270725
\]

### Step 2: Favorable Outcomes
To get exactly 4 queens, there is only **1 possible way** to select all 4 queens since there are exactly 4 queens in the deck:

\[
\text{Favorable outcomes} = \binom{4}{4} = 1
\]

### Step 3: Probability Calculation
The probability is the ratio of favorable outcomes to the total number of outcomes:

\[
\text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{270725}
\]

Thus, the probability of drawing all 4 queens is:

\[
\boxed{\frac{1}{270725}}
\]

Would you like further clarification on this? 

Here are 5 related questions to explore:
1. What is the probability of drawing 2 queens and 2 kings from a deck of 52 cards?
2. What is the probability of drawing 4 cards, none of which are queens?
3. How many ways can you draw 2 queens from a deck of 52 cards?
4. What is the probability of drawing exactly 1 queen in 4 draws?
5. What is the probability of drawing 4 aces from a 52-card deck?

**Tip**: When calculating combinations, remember that order doesn't matter in these types of problems, which is why we use the binomial coefficient.

Four cards are drawn at random from a standard playing pack of fifty two cards. Find the probability that the random draw will yield the 4 queens.

Explore how to calculate the probability of drawing all 4 queens from a standard deck of 52 cards. This problem delves into key probability and combinatorics concepts, utilizing the combination formula to determine the total and favorable outcomes. A perfect example for Grades 10-12 math students.

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