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On the occasion of the Dipawali festival, each student of a class sends a greeting card to every other student. If there are $20$ students in the class, the total number of greeting cards sent by the students is:

How many $6$-digit numbers can be formed using the digits of the number $112233$?

The number of six-letter words (with or without meaning) formed using all the letters of the word $VOWELS$ such that all the consonants never come together is ... .

$10$ men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

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