1. An ice cream shop offers sugar cones, waffle cones, or cake cones. The sugar

Question

1. An ice cream shop offers sugar cones, waffle cones, or cake cones. The sugar cones come in two sizes,
the waffle cone comes in one size and the cake cones come in three size.
(a.) How many cone options does the parlor offer?
(b.) A small ice cream order comes with 1 scoop of ice cream and a cone. The ice cream flavors are
vanilla, chocolate, strawberry, mint chip, or buttercrunch. How many choices does a customer have for
a small ice cream cone order?
(c.) Suppose that the ice cream shop also offer a choice of 3 toppings: chocolate syrup, caramel syrup
or marshmallow topping. How many choices are there for a small ice cream order with 1 topping? (d.)
For a medium ice cream order, customer can choose 2 scoops of ice cream (no topping). How many
choices for the order are there, if the customer wants two different flavors of ice cream?
2. How many numbers in the range 1000

Explanation / Answer

1. a) 3*4*3*2 = 72

b)4C2 * 3*2= 36

c)5

d)72*5*2= 720

2) There are total 9000 numbers in that interval

a)9 numbers have same digits repeated 4 times e.g. 1111,2222,3333... ,9999

so 9000-9=8991

b)1000 numbers (7000-7999)

c)begins with a 7 so thousands place is fixed.

Hundeds place has 9 options(7 is already taken)

Tens place has 8 option and unit place has 7 options

so 9*8*7 = 504

d)If it has 4 at thousands place

then from rest 3 places 2 have to be 4 and trhe other one any other digit from remaining 9 digits.

So 3C2*9 =27

If it doesn't have a 4 in thousand place then it start with 1 or 2 or 3 or 5 or 6.. or 9 .. so 8 options

so 27+8 = 35

3)

a)26^5 = 11881376

b)52^5 = 380204032

c)52^4 * 10 =73116160

d)5C1*10 * 52^4 =365580800

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