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In how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together?

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

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

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?

In how many ways can the letters of the word 'LEADER' be arranged?

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?

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

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?

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?

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 different ways can the letters of the word MATHEMATICS be arranged so that the vowels always come together?

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 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 a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

How many words with or without meaning, can be formed by using all the letters of the word. “DELHI’ using all the letters of the word ‘DELHI’ using each letter exactly once?

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

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

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:

In how many ways can the letters of the word LEADER be arranged?

How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

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

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

How many total numbers of not more than 20 digits that can be formed by using the digits 0 ,1 ,2 ,3 , and 4 is

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