sally has a bag of mixed lollies.The bag contains toffees,mints,fruit drops,smarties,jelly beans,candies and licorice.Sally allows every one in her class to choose 3 lollies,but they must not choose more than one of each kind.How many different combinations of lollies are possible?

Charls/Anthony/Nicky/Jade/Karen -- please use the same name for your posts.

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To solve this problem, we can use a combination formula.

Since the class is allowed to choose 3 lollies, and they must not choose more than one of each kind, we need to select 3 different types of lollies from the given options.

The formula to calculate the number of combinations is:

C(n, r) = n! / (r! * (n - r)!)

Where:
- n is the total number of options (in this case, the number of lollies)
- r is the number of selections to be made (in this case, 3)

Let's calculate the number of combinations:

We have 7 different types of lollies: toffees, mints, fruit drops, smarties, jelly beans, candies, and licorice. So, n = 7.

We need to select 3 different types of lollies, so r = 3.

Plugging these values into the formula:

C(7, 3) = 7! / (3! * (7 - 3)!)
= 7! / (3! * 4!)

Now, let's calculate each factorial:

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
3! = 3 * 2 * 1 = 6
4! = 4 * 3 * 2 * 1 = 24

Now, substitute these values into the formula:

C(7, 3) = 5040 / (6 * 24)
= 5040 / 144
= 35

Therefore, there are 35 different combinations of lollies possible.

To find the number of different combinations of lollies Sally's classmates can choose, we need to consider the different types of lollies available.

From the information given, we know that Sally has toffees, mints, fruit drops, smarties, jelly beans, candies, and licorice.

To calculate the number of combinations, we need to determine how many choices are available for each of the three positions (since each classmate can choose 3 lollies).

For the first position, there are 7 options (one from each type of lolly available).
For the second position, there are 6 options (as no lolly can be chosen more than once).
For the third position, there are 5 options.

To find the total number of combinations, we multiply the number of choices for each position:

Total combinations = 7 x 6 x 5 = 210

Therefore, there are 210 different combinations of lollies that Sally's classmates can choose.

sally has a bag of mixed lollies.The bag contains toffees,mints,fruit drops,smarties,jelly beans,candies and licorice.Sally allows every one in her class to choose 3 lollies,but they must not choose more than one of each kind.How many different combinations of lollies are