6. Suppose you need to enter a 4 digit code to enter a room. (a) How many such codes exists if there are no digits appear twice in your code? (b) How many such codes have exactly 1 digit which appears twice? (c) Now suppose you need to press 4 different digits simultaneously in order to unlock the door. Does the order matter? How many such codes exist?
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.
6. Suppose you need to enter a 4 digit code to enter a room.
(a) How many such codes exists if there are no digits appear twice in your code?
(b) How many such codes have exactly 1 digit which appears twice?
(c) Now suppose you need to press 4 different digits simultaneously in order to unlock the door. Does the
order matter? How many such codes exist?
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
