mark makes easter eggs.each egg contains 6 toffees,the toffees being selected from 3 different sorts.how many different selections are possible if each egg must contain at least one toffee of each sort?

Well, how about we crack this puzzle like an egg? Since each egg must contain at least one toffee of each sort, we can start by picking one toffee from each sort. That leaves us with three toffees to choose freely.

Now, for each of those remaining toffees, we have three possible sorts to pick from. So, for each toffee, we have 3 choices. Since there are three toffees, that means we have 3 choices for each toffee, three times over.

To find the total number of different selections, we can simply multiply the number of choices together. So, 3 choices for the first toffee, multiplied by 3 choices for the second toffee, multiplied by 3 choices for the third toffee, gives us:

3 x 3 x 3 = 27

Therefore, there are 27 different possible selections for each egg. Hoppy calculating!

To find the number of different selections possible, we can use a method called partitioning and distribution.

Since each Easter egg must contain at least one toffee of each sort, we can begin by distributing one toffee from each of the three sorts to each egg. This leaves us with 3 toffees that we need to distribute among the eggs.

To find the number of different distributions for the remaining 3 toffees, we can use stars and bars technique. We need to distribute the 3 toffees among the 3 eggs, so we can use 2 dividers to separate them. This can be represented as:

* | * | *

The stars represent the toffees, and the bars represent the dividers.

To find the different selections, we need to find the number of ways to arrange the stars and bars. In this case, we have 3 stars and 2 bars, so the number of different arrangements is given by the formula:

(N+C)!

where N is the total number of items (3 stars + 2 bars) and C is the number of bars (2). So we have:

(3+2)! = 5! = 120

Therefore, there are 120 different selections possible if each Easter egg must contain at least one toffee of each sort.

To determine the number of different selections of toffees for each egg, we can use a technique called combinations.

Since each egg must contain at least one toffee of each sort, we can distribute one toffee of each sort to each egg first. This leaves us with three additional toffees to distribute among the three eggs.

To calculate the number of selections, we can use the stars and bars method. Imagine that the three additional toffees are represented by stars, and we want to place bars to separate them into three different groups (the three eggs).

For example, if we have three stars and two bars, the arrangement would look like this: **|*|. This arrangement corresponds to distributing the three remaining toffees among the three eggs: the first egg has two toffees, the second egg has one toffee, and the third egg has zero toffees.

The number of possible arrangements of the stars and bars can be calculated using the formula:

(n + k - 1) C (k - 1),

where n is the number of stars (toffees) and k is the number of bars (groups). In this case, n = 3 and k = 2.

Plugging in the values into the formula, we have:

(3 + 2 - 1) C (2 - 1) = 4 C 1 = 4.

Therefore, there are 4 different selections possible if each egg must contain at least one toffee of each sort.