An engineer is putting together a train with 5 box cars, 3 tank cars, and 4 flat cars. For the box cars he will choose 5 from a group of 10 cars. For the tank cars he will choose 3 from a group of 5 cars. For the flat cars he will choose 4 from a group of 9 cars. How many different combinations are possible for the group of 12 cars selected?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Step by step
Solved in 2 steps with 1 images
