How many different 3-digit numbers can be formed with the digits 1, 2, 4, 6, and 8? How many of them are smaller than 300?

Q: How many 4 digit numbers do not have digit 0 in them.

A:

Q: How many integers from 1 through 1000 are multiples of 7 or multiples of 4?

A: Let A be the set of integers that are multiples of 7 and B be the set of integers that are multiples…

Q: How many six-digit license plates can be made if no plate begins with 0 or 6

A:

Q: How many different 11-letter words (real imaginary) can be formed from the letters in the word…

A: We have to find the total number of 11-letter words that can be formed from the letter in the word…

Q: How many different license plates can be made by using two letters followed by three digits selected…

A: The licensing plate should contain 5 places in which first 2 positions filled with letters and next…

Q: How many different seven-digit telephone numbers can be formed if the first digit cannot be zero?

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.