The answer is 24.

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The key to this answer is in the wording of the question - there are four different flavors of ice cream on the cone - meaning no flavor can appear more than once on the cone.

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This particular problem is called a Permutation, and is mathematically expressed as nPr, meaning how many ways can you order n things when selecting r things at a time. The calculation of a permutation is:

nPr = n! / ((n - r)!)

where '!' is the factorial function.

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In this particular question, both n and r equal 4 - there are 4 things, and you are selecting 4 of them at a time. so, the expression equates to:

4P4 = 4! / ((4 - 4)!) = 24 / 1 = 24

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Or, we can arrange the four things in groups of four, and see how many permutations there are. Let's reptesent the four ice cream flavors with the letters a, b, c, and d. When we look at how many ways we can order the four flavors when selecting four at a time, we get the following list of permutations:

1 a,b,c,d

2 a,b,d,c

3 a,c,b,d

4 a,c,d,b

5 a,d,b,c

6 a,d,c,b

7 b,a,c,d

8 b,a,d,c

9 b,c,a,d

10 b,c,d,a

11 b,d,a,c

12 b,d,c,a

13 c,a,b,d

14 c,a,d,b

15 c,b,a,d

16 c,b,d,a

17 c,d,a,b

18 C,d,b,a

19 d,a,b,c

20 d,a,c,b

21 d,b,a,c

22 d,b,c,a

23 d,c,a,b

24 d,c,b,a

As we can see, there are 24 permutations.

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If we were allowed duplicates, that is, any arrangement of flavors, where a flavor could occur none, once, twice, three times, or even four times, then the answer would be 256. In this case, the mathematical expression is

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S = an

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where 'a' is the set of things chosen (ice cream flavors) and 'n' is the number of times it is selected. In this case, both n and a are 4, so the equation works out as follows.

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S = 44 = 256.

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If we were to list the possible arrangements, it would be as follows.

1 a,a,a,a

2 a,a,a,b

3 a,a,a,c

4 a,a,a,d

5 a,a,b,a

6 a,a,b,b

7 a,a,b,c

8 a,a,b,d

...

252 d,d,c,d

253 d,d,d,a

254 d,d,d,b

255 d,d,d,c

256 d,d,d,d

How to make cupcakes; general instructions for making cupcakes:

Basic Cupcake Mix

The basic mixture for a cupcake recipe is the same as for many other large sponge cake recipes with the basic mixture consisting of

50g/2oz self raising flour

50g/2oz Caster sugar (superfine)

50g/2oz Butter or margarine (shortening)

1 Egg

These quantities are enough to make about 6 medium or 10 very small cupcakes, about 5cm/2-inches in diameter and can be doubled or trebled as required, however make sure to keep the same proportions of ingredients i.e. if you wish to treble it the amounts would be

150g/6oz Self Raising Flour

150g/6oz Caster Sugar (superfine)

150g/6oz Butter or Margarine (shortening)

3 eggs

Mixing the cupcake ingredients

Although the traditional method is to cream together the butter and sugar, then add the egg, mixing well, before adding the flour, good results can be achieved by just placing all the ingredients in the mixing bowl at the same time (with the exception of any additional fruit if using) as does mixing the cupcake ingredients in a food mixer or processor.

How much mixture to put in the cupcake paper case or tin

A level tablespoon in each paper case will make medium sized cupcakes about 7.5cm/3-inches in diameter. A heaped teaspoon of cupcake mixture in each paper case or cupcake hole will make small cupcakes about 5cm/2-inches in diameter. You can make larger and deeper cupcakes by placing more of the cupcake mixture in the cases or cupcake hole however, never fill the case or hole more than 2/3rds full.

At what oven temperature should cupcakes be cooked ?

In general 190C, 375F, Gas Mark 5 although if you have a fan assisted oven, you should reduce the temperature accordingly.

For how long should cupcakes be cooked?

If you are using the above guidelines or a heaped teaspoon of cupcake mixture per cake, 15 minutes should be long enough however, you can test whether the cupcake is cooked through by pushing a wooden toothpick into the centre. If it comes out clean, then the cupcake mixture has cooked through. If you decide to make slightly larger cupcakes, they will need an extra 5 minutes or so.

Decorating Cupcakes - How to decorate Cupcakes

Before you decorate your cupcakes, it is important to allow them to cool completely by removing them from the baking sheet or tin, and placing on a wire rack. Once cool, the options are endless, but here are just a couple of ideas for decorating cupcakes.

Light Glacé icing or frosting

Simply mix icing sugar (confectioners Sugar) with a very little water until the mixture is smooth but not too runny, then spread thinly over the tops of the cupcakes. Flavourings can be added to the icing mixture such as lemon, orange or coffee, as can colourings and you can sprinkle the icing with chocolate vermicelli, hundreds and thousands or small sweets before it sets on the cupcake. Click here for lots of Glace Icing Recipes.

Butter cream (butter icing)

Mix up your favourite butter cream flavour and spread or pipe on the tops of the cupcakes. Click here for lots of Butter Cream recipes. As with the simple icing above, further decorations can be pressed into the butter icing.

Fairy cake wings

Once the cupcakes are cold, cut a thin slice from the tops and cut them in half down the centre. Place a teaspoon of jam or butter cream (butter icing) on top of the cut surface of the cupcake then set the two cut pieces into the jam or butter cream at an angle to form wings.

Or, the simple way to make cupcakes:

Use any type cake recipe or purchase a good cake mix (your favorite flavor), purchase cup cake papers. If you don't have a muffin or cup cake baking pan, you can use a regular baking pan with sides at least two inches high.

Place the cup cake papers in the pan; if you're using a regular pan, place them thight enough for each to hold up the sides of the papers when you pour the batter into them. If the sides of the paper cups aren't supported, you will end up with giant cookies.

Mix the batter according to the recipe or the instructions on the box of mix. Pour it into the cup cake papers about half way filled. Bake according to the recipe or instructions. You can eat them warm, right out of the oven. Or, if you want to frost them be sure to let them cool thoroughly first and use any frosting that you like.

No, BK fast-food restaurants, do not sell Lemonade Icees. BK only serves Cherry & Coca-Cola (Coke) ICEEs.

Source(s):

My Last BK Dine-In