46.
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?

47.
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?

48.
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

49.
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

50.
20 men handshake with each other without repetition. What is the total number of handshakes made?

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