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

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?

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 in the committee. In how many ways can it be done?

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

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

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?

In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?

There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?

How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

A coin is tossed 3 times. Find out the number of possible outcomes.

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