# A Game of cards with Mr. 11 ...

**Discrete Mathematics**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 \(\color{Red}{❤}\),Diamonds \(\color{Red}{♦}\) ,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)