For this problem, assume gwen and harry have 5 types of cones and 9 flavors of ice cream.
(1) in how many different ways can your order one cone and two scoops of ice cream? (as in the book, putting one flavor on top of another is different from putting them the other way around.)
(2) in how many different ways can your order one cone and two scoops of ice cream which are not the same flavor?

Hello!

In this problem you can chose 3 options:

the type of cone, the first flavour, and the second flavour.

a) In how many different ways can your order one cone and two scoops of ice cream?

You have 5 options for cones, 9 options for the first ball of ice cream, and 9 options for the second ball of ice cream (because you can repeat flavour) then the total number of combinations is the product of this 3 numbers, this is:

5*9*9 = 405 combinations

b) Here we cant order the same flavour of ice cream, then:

we still have 5 options for cones, 9 options for the first ball of ice cream, and this time 8 options for the second ball ( because we need to remove the flavour that we picked in the first ball of ice cream) then the number of combinations is:

5*9*8 = 360 combinations.

third choice down

step-by-step explanation:

the first inequality is based on the number of adults and campers, and the second inequality is based on the cost of feeding both the adult and the camper.

we know that there is room for 525 people max.   it's ok to have less than 525, but it's not ok to have more than 525, so the inequality is less than or equal to.   the number combination of adults (x) and campers (y) cannot exceed this 525 max.   therefore:

x + y ≤ 525

now we talk about cost.   it costs $9 to feed one adult, so depending upon the number of adults you have (x) depends upon how much it will cost to feed that number of adults.   same with the campers, who cost $5 to feed.   the adults can be represented by 9x and the campers can be represented by 5y.   since the budget cannot exceed 1,200, the second inequality is:

9x + 5y ≤ 1200