Question
Help Please
Among 150 math students 42 have taken Discrete Math, 32 have taken History of Math. There are 10 have taken both. How many students have taken only Discrete Math, but not History of Math? How many students have taken only History of Math, but not Discrete Math? How many students have taken only one of Discrete Math or History of Math? How many students have taken neither course? How many stuents have taken at least one of Discrete Math or History of Math (possibly both)? 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. How many cone options does the parlor offer? 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 butter crunch. How many choices does a customer have for a small ice cream cone order? 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? 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? How many numbers in the range 1000 - 9999 do not contain the same digit 4 times? end with the digit "3"? end with a "3" and have no repeated digits? have exactly two digits that are 7s? Suppose that a password for a computer system must have exactly 6 characters. How many passwords are possible that only use lower-case alphabetic characters? How many passwords are possible that can use either upper and lower-case characters? 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? 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? In a classroom of 20 students, show that there are at least two students with the birthdays in the same month. Suppose there is a class and that an assignment is worth 100 points. Possible scores range from 0 to 20. How- many student must be in the class in order to guarantee that that at least two students receive the same score on the assignment?
Explanation / Answer
4)
no. of alphabetical characters = 26
a) 26^6
b) 52^6
c) 10*52^5
d) 6*10*52^5 = 60*52^5
5) There are 12 months and 20 students .. so by pegion hole theorem there are atleast ceil(20/12) = 2 students with the birthday in the same month
6) atleast 22 students (since 21 ways of scoring can be done from 0 - 20)
