Question

At an ice cream store, there are 6 flavors of ice cream: banana, strawberry, vanilla, mint, chocolate and raspberry. How many different 2- flavor ice cream cones can be made? (5 points)

Steve has 6 pants and 7 shirts in his closet. He wants to wear a different pant/shirt combination each day without buying new cloths for as long as he can. How many weeks can he do this for? (5 points)

Answer 1

Solution:

1) There are total of 6 flavors available. 2-flavor ice cream cones are to be made. If each cone must have mix of 2 flavors and each cone should be different, means the repetition is not allowed and order doesn't matter (that is if a cone is made by mix of first banana and then strawberry flavor or first strawberry and then banana flavor, they will be counted as one).

So, the number of different combinations = using combinations formula, nCr where n = 6 and r = 2

6C2 = 6!/(2!*(6 - 2)!)

Number of different combinations = 6*5*4!/(2*1)*4! = 15 different combinations

2) 6 pants and 7 shirts should make different combinations for each day. Note that each shirt can be wore with a pant, giving different combination always. So, one pant can make 7 different combinations (by wearing with 7 different shirts). With 6 different combinations, such 7 different combinations can be made 6 times. So, total number of possible combinations = 6*7 = 42 combinations

This means that Steve can have a different combination for 42 days,without having to buy new clothes. So, with 42 days, such different combinations can be made for 42/7 = 6 weeks (since each week has 7 days)

So, Steve can do this for 6 weeks.