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?

There are 8 Orange, 6 White and 7 Black pens in a Parul Bag. Parul picked up randomly a pen. What is the probability that it is neither orange nor white?

In how many ways a committee consist of 8 men and 2 women can be formed from 12 men and 5 women?