How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

How many words, no matter if they are meaningless, can be formed by the letter, of the word ‘DIARY’?

How many numbers lying between 100 and 1000 can be formed with digits 0,1,2,3,4,5 if repetition is not allowed?

How many words can be formed from the letters of the word 'ENGINEER'?

Four digit numbers are formed by using the digits 1, 2, 3, 5 without repetition of digits. How many of them are divisible by 4?

How many words can be formed from letters of the word 'ULTRA' so that the vowels never come together?