How many 5-number license plates can be made using the digits 1,2,3,4,5,6,7, if an odd digit must come first and a. repetitions are allowed b. repetitons are NOT allowed

Q: Standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed…

A: we know thatno.of letters (A to Z)=26no.of digits(0 to 1)=10

Q: How many 5-number license plates can be made using the digits: 0, 1, 2, 3, 4, 5, if repetitions are…

A: Given that 5-number license plates that are made using digits 0, 1, 2, 3, 4, 5. We have to determine…

Q: How many different standard plates are possible in this system?

A:

Q: A license plate is to consist of 3 digits followed by 5 uppercase letters. Determine the number of…

A:

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.