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Mathematic question

Can someone help me present a point to beginning players about why a double of RHO's opening bid should be a takeout double as opposed to a penalty double?  The way I will state the problem below is to flush out some example hands I will be presenting.

Assume RHO opens 1M.  Under RHO's partnership agreements, RHO has promised at least 5 cards in the opened major suit.

What are the chances that the next player owns exactly the number of cards shown below in the opened major?  

-- exactly 6 cards

-- exactly 5 cards

-- exactly 2 cards

-- exactly 1 card

-- exactly 0 cards

Thank you, in advance.

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