A cupcake shop produces 5 types of cupcakes, one of which is chocolate. Assume there is a large amount available of each type of cupcake.

1/ How many different selections of 8 cupcakes are there?

2/ How many different selections of 8 cupcakes have at least 3 chocolate cupcakes?

3/ How many different selections of 8 cupcakes have at most 2 chocolate cupcakes?

1) 390625, 2) 1365, 3) 411105.

Step-by-step explanation:

Since we have given that

Number of types of cupcakes = 5

Number of chocolate type = 1

1/ How many different selections of 8 cupcakes are there?

Number of cupcakes we need to select = 8

Since we have 5 options for each 8 cupcakes.

So, the number of ways to select 8 cupcakes would be :

2/ How many different selections of 8 cupcakes have at least 3 chocolate cupcakes?

Number of different selection would be :

=

3/ How many different selections of 8 cupcakes have at most 2 chocolate cupcakes?

Number of ways to select no chocolate + Number of ways to select 1 chocolate + Number of ways to select 2 chocolate

Hence, 1) 390625, 2) 1365, 3) 411105.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

nlgqer

step-by-step