Discrete Math

How many ways can 10 people, consisting of 6 men and 4 women, stand in line without any restrictions?

How many ways can 6 men stand in line such that no two women are next to each other if there are 4 women in total?

How many ways can 6 men and 4 women stand in line such that no two men are next to each other, knowing it is impossible due to the pigeonhole principle?

How many binary strings contain exactly 5 zeros and 14 ones where each zero must be followed immediately by two ones?

How many ways can you arrange the letters in the word 'hello'?

There are five people A, B, C, D, E but only four chairs. Person B has to sit in the second chair. How many ways can the people be seated?

In how many ways can 5 men and 3 women be arranged in a row if no two women are standing next to one another?

In how many ways can the letters in the word SUCCESS be arranged if no two S's are next to one another?

How many socks must be randomly removed from the drawer to ensure that two green socks are drawn?

How many socks must be randomly removed from the drawer to ensure that three of every colored sock have been drawn?

How many socks must be randomly removed from the drawer to ensure that four of one of the colors has been drawn?

If the theater holds 1,300 people, how many of those seats need to be filled to ensure that at least two people have the same first and last initials?

By selecting 10 points on an equilateral triangle with side length 1, show that there are at least two points with distance less than or equal to $\frac{1}{3}$ apart.

Find the power set of the set $A = \{ 1, 2, 3 \}$.

Find two sets $A$ and $B$ such that $A$ is an element of $B$ and $A$ is a subset of $B$.

Determine if the following sets are power sets of some unknown set. For example, for a given set, check if it can be the power set by checking the number of elements which should be a power of two.

Rewrite the English sentence "There is an adult in your neighborhood who knows kung-fu and karate" using predicates and quantifiers.

Rewrite the English sentence "There is an adult in your neighborhood who knows kung-fu but not karate" using predicates and quantifiers.

Rewrite the English sentence "Every adult in your neighborhood knows kung-fu or karate" using predicates and quantifiers.

Rewrite the English sentence "No adult in your neighborhood knows kung-fu or karate" using predicates and quantifiers.