A shoe has twelve eyelets. A shoelace can go through each eyelet in two different ways: one way going in/toward the shoe, and another way coming out/away from the body of the shoe through the eyelet away from the shoe. After we get the shoelace through an eyelet, we must put the shoelace through a different eyelet (in/toward or out/away from the shoe), until the shoelace passes through all twelve eyelets once, and no more than once. How many (different) ways are there to tie the shoelace to the shoe in this procedure?
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.
A shoe has twelve eyelets. A shoelace can go through each eyelet in two different ways: one way going in/toward the shoe, and another way coming out/away from the body of the shoe through the eyelet away from the shoe. After we get the shoelace through an eyelet, we must put the shoelace through a different eyelet (in/toward or out/away from the shoe), until the shoelace passes through all twelve eyelets once, and no more than once. How many (different) ways are there to tie the shoelace to the shoe in this procedure?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
