To solve this problem, we need to calculate the probability that, when Henry opens 4 packets, he gets one aeroplane of each colour. Since there are four colours (red, yellow, green, and blue) and equal numbers of each colour are distributed, the probability of getting a specific colour from a packet is equal for each colour.

Assumptions:

• There are 4 colours of aeroplanes: red, yellow, green, and blue.
• Each colour has an equal probability of $\frac{1}{4}$ of being chosen.
• Henry opens 4 packets, and we need to calculate the probability of getting exactly one aeroplane of each colour.

Step 1: Total possible outcomes

Since each packet contains one aeroplane, and Henry opens 4 packets, the total number of possible outcomes (with no restrictions on the colours) is:

$4 \times 4 \times 4 \times 4 = 4^4 = 256$

This represents all possible combinations of aeroplanes he could get from opening 4 packets.

Step 2: Favorable outcomes (one aeroplane of each colour)

To have one aeroplane of each colour (red, yellow, green, and blue), Henry needs to get exactly one of each colour in some order. The number of ways he can choose one aeroplane of each colour from the 4 packets is the number of different permutations of the 4 colours. This is simply the number of ways to arrange 4 distinct colours, which is:

$4! = 4 \times 3 \times 2 \times 1 = 24$

Step 3: Probability

The probability is the ratio of favorable outcomes to total outcomes:

$P(\text{one aeroplane of each colour}) = \frac{24}{256} = \frac{3}{32}$

Final Answer:

The probability that Henry opens 4 packets and gets one aeroplane of each colour is $\frac{3}{32}$.

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Would you like further explanation or details on another aspect of probability? Here are some related questions:

1. What would happen if Henry opened 5 packets instead of 4?
2. How would the probability change if the colours were not equally distributed?
3. How can we calculate probabilities for non-equal outcomes (e.g., if there are more red aeroplanes than yellow)?
4. What is the probability of Henry opening 4 packets and getting at least one yellow aeroplane?
5. How does this problem relate to the concept of sampling with or without replacement?

Tip: In probability problems involving equal chances, it's often useful to calculate the total number of possible outcomes first and then figure out how many ways the favorable events can occur.