1. How many 5-digit license plate numbers can we generate from the numbers, 0, 1, 2, 3, and 4 if it cannot start with 0.
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.
Back Check your Understanding I. answer the following.
1. How many 5-digit license plate numbers can we generate from the numbers, 0, 1, 2, 3, and 4 if it cannot start with 0.
2. A social media account requires a 6-character password. Passwords should only contain numbers from 1 to 9 and capital letters A to E. How many different passwords can you generate
a. if the characters should not repeat?
b. if the characters repeat?
c. if the first 3 characters are numbers and the last 3 characters are letters, which are all distinct?
3. Which of the illustrates a permutation? A. Selecting a set of JS Prom committee consisting of 8 members from 20 people. B. Selecting a set of JS Prom committee consisting of a chairman, vice chairman, and promotion head from 20 people.
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