sarah has a bag of mixed lollies.T?he bag contains toffees,mints,fruit drops,smarties,jelly beans,candies and licorice.She allows everyone 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 ? Is it 7^3=21 thanks
No, the total number of different combinations of lollies is not 7^3.
Since each student can choose 3 lollies and there are 7 different types of lollies, we need to use the concept of combinations without repetition.
To calculate the total number of different combinations, we can use the formula for combinations without repetition, which is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items chosen.
In this case, n = 7 (the total number of different types of lollies) and r = 3 (the number of lollies chosen by each student).
Using the formula, we can calculate the combinations as follows:
7C3 = 7! / (3!(7-3)!) = (7 x 6 x 5) / (3 x 2 x 1) = 35
Therefore, there are 35 different combinations of lollies that are possible.
To find the number of different combinations of lollies, we need to consider several factors.
First, let's look at the number of different types of lollies Sarah has: toffees, mints, fruit drops, smarties, jelly beans, candies, and licorice.
For the first lolly choice, there are 7 options.
For the second lolly choice, there are 6 options remaining (as they should not choose the same type as the first choice).
For the third lolly choice, there are 5 options remaining (as they should not choose the same type as the first and second choices).
To find the total number of combinations, we need to multiply the number of options for each choice together:
7 * 6 * 5 = 210
Therefore, there are 210 different combinations of lollies possible.
So, the correct answer is not 7^3, but 7 * 6 * 5 = 210.