Assume that every time you buy an item of the Hong Kong Disney series, you receive one of the

four types of cards, each with a cartoon character Mickey, Minnie, Donald and Daisy with an equal
probability. Over a period of time, you buy 6 items of the series. What is the probability that you will
get all four cards?

165/1024

To find the probability of getting all four cards, we can use the concept of combinations.

First, let's calculate the total number of possible outcomes. Since there are four types of cards and each has an equal probability of being received, we have a total of 4 possible outcomes for each item.

Therefore, the total number of possible outcomes for the 6 items can be calculated as:

4 x 4 x 4 x 4 x 4 x 4 = 4^6 = 4096

Next, let's calculate the number of favorable outcomes, which is the number of ways to get all four cards.

Since there are 4 types of cards, one way to obtain all four cards would be to have one of each type. This can be done in a specific order, so the number of favorable outcomes is:

4 x 3 x 2 x 1 = 24

Now, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 24 / 4096 = 1 / 170

So, the probability of getting all four cards after buying six items from the Hong Kong Disney series is 1 in 170.