Probability: Number of Cases

When a card is drawn out of cards with natural numbers from to , find the number of cases that a card with either multiples of or prime numbers is drawn.

When a card is drawn from the cards with natural numbers from to , find the number of cases in which a card with either a multiple of or a multiple of is drawn.

When two different dices are rolled at the same time, find the number of cases in which the sum of numbers is or the difference of numbers is . (note: the dices are cubic)

When making combo menus by selecting one hamburger and one side menu from kinds of hamburgers and kinds of side menus, find out how many combo menus can be made.

A mountain has courses to reach the top. When you come down after reaching the top, you're going to come down on a different route. Find out how many ways you can track on the mountain in that case.

Find the number of cases where friends try to run in order.

A family of , a couple and children, are trying to take a family photo. When taking a picture in a row, find the number of cases where a couple takes a picture next to each other.

Find the number of cases where Melody stands in the front and Riley stands in the back when people, including Melody and Riley, stand in a line.

Find the number of natural numbers in three digits that can be made by drawing cards from each of the cards with the numbers .

Find the number of multiples of of the four-digit natural numbers that can be made by drawing cards from cards each with natural numbers from to .

Find the number of cases in which the chairman, vice chairman, and general secretary are elected from candidates.

A second-year middle school class tries to select one goalkeeper and one striker each as a representative player for the school soccer tournament. Find the number of cases to select the representatives from applicants for the positions.

Find the number of cases in which one president and two vice presidents are elected from candidates.

When electing three class representatives from students, including Antonio, find the number of cases where Antonio is elected.

Find out how many times a total of baseball teams will play each other once.

principals from the schools in a region gathered, find out how many times they have to shake hands to greet all of them.

When electing two representatives from male students and female students, find the number of cases in which more than one male student is included as a representative.