1) Leo visits a salad bar and has a choice of 3 types of leafy greens: iceburg l

Question

1) Leo visits a salad bar and has a choice of 3 types of leafy greens: iceburg lettuce, red leaf lettuce, or
spinach. She may choose from four chopped vegetables: carrots, onions, chickpeas, or corn. There are
3 salad dressings: ranch, blue cheese and italian. There are 2 toppings: croutons or almonds.
(a.) How many salads are possible, assuming that Leo chooses a leafy green, a chopped vegetable, a
salad dressing and one topping?
(b.) Suppose Leo orders a deluxe salad and chooses a leafy green, two di erent chopped vegetables, a
salad dressing and one topping. How many deluxe salads are possible
(c.) Now suppose that Leo would like to include a beverage. His choices for beverages are: soda
(small, medium, large), co ee, or bottled water. How many beverage choices are there? (d.) For a
super combo lunch, Leo can choose a regular salad (chooses a leafy green, a chopped vegetable, a salad
dressing and one topping), a beverage and one of two cookies (buttercrunch or chocolate chip). How
many combo lunches are possible?

2. How many numbers in the range 1000-9999
(a.) do not contain the same digit 4 times?
(b.) begin with the digit "7"?
(c.) begin with a "7" and have no repeated digits?
(d.) have exactly three digits that are 4s?

3. Suppose that a password for a computer system must have exactly 5 characters.
(a.) How many passwords are possible that only use lower-case alphabetic characters?
(b.) How many passwords are possible that can use either upper- and lower-case characters?
(c.) How many passwords are possible that use a combination of upper- and lower-case characters as
well as exactly one numeric digit in the last position?
(d.) How many passwords are possible that use a combination of upper- and lower-case characters as
well as exactly one numeric digit if the position of the numeric digit is variable?

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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