In how many different ways can the letter of the word ‘AVERGE’ be arranged so that the vowels always come together?

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?

In how many ways can 6 green toys and 6 red toys be arranged, such that 2 particular red toys are never together whereas 2 particular green toys are always together?

In how many ways can the letters of the word ’RUMOUR’ be arranged

There are 6 boxes numbered 1,2,...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:

How many 4 letter words with or without meaning can be formed out of letters of the word. ‘LOGARITHMS, if reptilian of letters is not allowed

An urn contains 5 red, 3 green, 2 blue and 4 yellow marbles. If three marbles are picked at random, what is the probability that at least one is yellow?

A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?

How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3, and 4, if repetition of digits is allowed?

How many five digits positive integers that are divisible by 3 can be formed using the digits 0, 1, 2, 3, 4, and 5, without any of the digits getting repeating?