Math Help Forum: Combinatorial Prob.

2 questions.

1. Joe, an avid and properly licensed sportsman, is in his hunting blind when he locates 20 canada geese, 25 mallard ducks, 40 bald eagles, 10 whopping cranes, and 5 flamingos. Joe randomly selects six birds to target. What is the probability that at least one of each species is targeted?


2. Thirty items are arranged in a 6 by 5 array as shown.



Calculate the number of ways to form a set of three distinct items such that no two of the selected items are i the same row or same column.

Hello, kangta27!

. .

Choose any of the 30 available numbers.
Cross out that number and any number in its row and in its column.
This leaves a array of numbers.

Choose any of the 20 available numbers.
Cross out that number and any number in its row and in its column.
This leaves a array of numbers.

Choose any of the 12 available numbers.

It seems that there are: . ways.

But the order of the selection of the three numbers is not considered.
Hence, we must divide by

Answer: . ways.

First question: