Three numbers are to be selected at random and without replacement from the five numbers 4, 5,7,8, and 11.What is the probability that the three numbers selected could be the lengths of the sides of a triangle?

There are 5!. or 120. ways of arranging 5 different solid-colored flags side by side. If the colors of the flags are red, blue，yellow，green, and orange，how many of those arrangements have either the red fag or the blue flag in the middle position?

k is randomly selected from the set of integers from 1 to 100, inclusive.​

REENA'S MOVIE COLLECTION The table above shows the number of movies in each genre in Reena's movie collection. If two different movies are to be selected at random from the collection. what is the probability that neither movie will be in the science fiction genre?

Several 0 and 1 are arranged in a 10*10 palace as follows. Among all the number 0, what is the probability that they are arranged in both an odd row and an odd column? Give your answer as a fraction.

There are 5!, or 120,ways of arranging 5 different solid-colored flags side by side. If the colors of the flags are red, blue,yellow, green, and orange,how many of those arrangements have either the red flag or the blue flag in the middle position?

Pat has five matched pairs of socks and no two of the pairs are the same color. If Pat selects two socks simultaneously and at random, what is the probability that the two socks selected will be a matched pair.

A box contains 100 purple balls, 100 red balls, and 100 white balls. What is the minimum number of balls that must be chosen to ensure that at least 4 of the balls chosen have the same color.

The cast of a certain play has 2 male characters and 2 female characters. The director of the play will select the 2 male characters from 6 male actors and the 2 female characters from 8 female actors. How many different sets of 4 actors, consisting of 2 male actors and 2 female actors, are there that can be selected by the director?

P is the set of all of all positive factors of 20, and Q is the set of all positive factors of 12. If a member of Pwill be chosen at random, what is the probability that the chosen member will also be member of Q .