A Game of cards with Mr. 11 ...

Probability Level 4

Satvik and Krishna are playing a game of cards. Both of them are holding one card in hand chosen from the deck . It's given that the number on Krishna's card is strictly greater than the number on Satvik's card.

The number of ways in which this can happen is $K$.

Find the remainder when $K$ is divided by $11$ .

Details and assumptions:-

$1.\quad$ A deck of card has 52 cards, which are divided into 4 suits (Hearts $\color{#D61F06}{❤}$,Diamonds $\color{#D61F06}{♦}$ ,Club $\clubsuit$ ,Spade $\spadesuit$). Each suit has 13 cards, which are {Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King}.

$2.\quad$ In this question, consider that the numbers assigned to cards are $\text{Ace=1,Jack=11,Queen=12,King=13}$ and others are numbered as they are already.

This problem is a part of the set 11≡ awesome (mod remainders)

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