You tell your friend about the strange farmer's market you've been to in the previous question, and so your friend decides to visit it the next day. Just like you, your friend has to pick 1 fruit (at random, without looking) from each of 3 bags: Bag A, Bag B, and Bag C. There are again only apples and oranges inside each of the bags, but now in the following quantities: Bag A contains 1 apple(s) and 5 orange(s), Bag B contains 4 apple(s) and 1 orange(s), Bag C contains 3 apple(s) and 1 orange(s). Given that your friend picked exactly 2 apples in total, what is the probability that the fruit picked from bag A was an apple?

Slimp's Bookstore receives a box of books from each of five paperback publishers. Each box contains 22 different titles. The store manager decides there is room to display 4 books from each of 3 of the publishers. How many ways can the display be chosen? (Round your answer to the nearest one billion.)

In a restaurant servers are constantly bringing out beverages to their tables. If a restaurant had a dining hall with only 4-seated tables, how many combinations of soft drinks could the servers bring out if they only had {Coke, Sprite, Fanta}?

A clerk at a bookstore is restocking a shelf of the best-selling novels. He has two copies each of the three different novels.   How many different ways can he arrange the books on the shelf? Assume each copy is identical.?   How many different ways can these books be arranged on the shelf if the copies of the same novel must be grouped together?

A birthday cake is to have two layers of cake separated by a layer of icing, with another layer of icing on top. There are 3 kinds of cake the chef knows how to make, and she may use either two different kinds or the same one twice for the two cake layers. The chef knows recipes for 4 different icings, and she will use two different recipes, one for each icing layer, in this cake. How many different cakes could the chef make? Note that the order of the layers matters, e.g. chocolate over strawberry is different from strawberry over chocolate.

There are 3 apples, 5 pears and 4 oranges in a basket. If a waiter were to line up these fruits side by side on a table, how many different ways could he order them?

A clerk at a bookstore is restocking a shelf of the best-selling novels. He has three copies each of the four different novels. How many different ways can he arrange the books on the shelf? Assume each copy is identical. How many different ways can these books be arranged on the shelf if the copies of the same novel must be grouped together?

How many different baseball bating line ups are possible if the coach wants to put one of the three best batters in the third position and the pitcher in the fifth position?

You have 4 indistinguishable gold coins and 4 indistinguishable silver coins. Each coin has a side that is heads and a side that is tails. You want to stack the eight coins on a table into a single stack so that no two adjacent coins are face to face. Find the number of possible distinguishable stacks of the 8 coins.

how many ways can 3 outfielders and 4 infidlers be chosen from 5 outfeilders and 7 infeilders?