Permutations - Permutations When Repetitions Are Allowed

How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are allowed?

Find the number of arrangements of the letters in the word BERMUDA so that consonants and vowels are in the same relative positions.

Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition. How many of these numbers are not divisible by 5?

Find the number of ways letters of the word HISTORY can be arranged if Y is next to T.

Determine the number of arrangements of letters of the word ALGORITHM if vowels are always together.

Determine the number of arrangements of letters of the word ALGORITHM if consonants are at even positions.

In a group photograph, 6 teachers are in the first row and 18 students are in the second row. There are 12 boys and 6 girls among the students. If the middle position is reserved for the principal and if no two girls are together, find the number of arrangements.

Find the number of ways letters of the word HISTORY can be arranged if Y and T are together.