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A game called housie (similar to Bingo) is played in India. This game is played by a group of people based on a few rules. I need to know how many unique tickets can be printed in one session of a Housie game.

How a ticket is made in a game of housie is as follows:

  1. Numbers are from 1 to 90.
  2. There are 3 rows in a ticket.
  3. There are 9 columns in a ticket.
  4. Each row has to have 5 unique numbers (not more not less).
  5. A column can have 0, 1, 2 or 3 numbers in it.
  6. 1st column can only contain number from 1-9, 2nd row can only contain numbers from 10-19, 3rd row can only contain numbers from 20-29 ....... 8th column can only contain numbers from 70-79 and the last 9th column can only contain numbers from 80-90

enter image description here

The above image is an illustration of how unique housie tickets looks like. With the above rules being applied, I need to know how many UNIQUE tickets can be printed from of this combination.


marked as duplicate by joriki probability Aug 22 '15 at 5:18

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Just for clarification: the 5th point is not necessary. Regarding the 6th point, do you speak about rows or do you mean rather columns? $\endgroup$ – Karel Macek Sep 22 '14 at 20:46
  • $\begingroup$ @karel - About the 6th point, I mean column itself and not row. $\endgroup$ – Nikhil Rao Sep 23 '14 at 10:43
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    $\begingroup$ You can edit your question and fix it. $\endgroup$ – Karel Macek Sep 23 '14 at 10:53
  • $\begingroup$ The question of which I marked this as a duplicate gives slightly different rules in that columns can't be empty and the numbers are in ascending order in the columns. Since a) your example cards all follow these additional rules, so it seems you may have just forgotten to specify them, and b) these rules can readily be omitted in mjqxxxx's answer to the other question if the omission was indeed intentional, mjqxxxx's answer provides a sufficient answer to this question. $\endgroup$ – joriki Aug 22 '15 at 5:24