Question 1192417
.
from the deck of 52 playing cards, how many ways can we choose 10 hearts and 10 diamonds?
~~~~~~~~~~~~~~~~~~~~



The solution by  @mananth  (note I do not call this person as a  " tutor ") 
is  TOTALLY  WRONG  and  FATALLY  INCORRECT.


I came to bring you a correct solution.



<pre>
    A "standard" deck of playing cards consists of 52 Cards in each of the 4 suits 
    of Spades, Hearts, Diamonds, and Clubs.  Each suit contains 13 cards: 
    Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.


So, 10 hearts from 13 hearts can be chosen in  {{{C[13]^10}}} = 286  different ways.

10 diamonds can be chosen from 13 diamonds  in  {{{C[13]^10}}} = 286  different ways.


These selections from different kinds of cards are independent.


Therefore, the total number of different selections the problem asks about is the product

    {{{C[13]^10*C[13]^10}}} = 286*286 = 286^2 = 81796.    <U>ANSWER</U>
</pre>

Solved.


--------------------


Ignore the post by @mananth for your safety.