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Basics of Counting problems in Discrete Math

Basics of Counting example question

How many positive integers between 50 and 100

a) Are divisible by 7? What are these integers?

b) Are divisible by 11? What are these integers?

c) Are divisible by both 7 and 11? What are these integers?

 

Solution to this Discrete Math practice problem is given in the video below!



Basics of Counting example problem #2

How many positive integers between 100 and 999 inclusive

a) Are divisible by 7?

b) Are odd?

c) Have the same three decimal digits?

d) Are NOT divisible by 4?

e) Are divisible by 3 or 4?

f) Are NOT divisible by either 3 or 4?

g) Are divisible by 3 but NOT 4?

h) Are divisible by 3 and 4?

 

Solution to this Discrete Math practice problem is given in the video below!



Basics of Counting example #3

How many strings of three decimal digits

a) Do NOT contain the same digit three times?

b) Begin with an odd digit?

c) Have exactly two digits that are 4s?

 

Solution to this Discrete Math practice problem is given in the video below!



Basics of Counting example question #4

How many functions are there from the set {1, 2, …, n}, where n is a positive integer, to the set {0, 1}

a) That are one-to-one?

b) That assign 0 to both 1 and n ?

c) That assign 1 to exactly one of the positive integers less than n ?

 

Solution to this Discrete Math practice problem is given in the video below!



Basics of Counting example problem #5

How many ways are there to seat six people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors?

 

Solution to this Discrete Math practice problem is given in the video below!






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