Answer
There are 10 outcomes in the event N.
Work Step by Step
Let N be the set of five cards in hearts that are not flushes. The set N is called a straight flush. There are 13 denominations in the deck that is (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A).
Suppose we are assuming all cards are hearts.
There are 10 possible straight flushes in a suit (A, 2, 3, 4, 5) to (10, J, Q, K, A). Here (A, 2, 3, 4, 5) is lowest straight and (10, J, Q, K, A) is highest straight.
The possible outcomes of the event N is:
\[N=\left\{ \begin{align}
& \left( A,2,3,4,5 \right),\text{ }\left( 2,3,4,5,6 \right),\text{ }\left( 3,4,5,6,7 \right),\text{ }\left( 4,5,6,7,8 \right),\text{ }\left( 5,6,7,8,9 \right), \\
& \left( 6,7,8,9,10 \right),\text{ }\left( 7,8,9,10,J \right),\text{ }\left( 8,9,10,J,Q \right),\text{ }\left( 9,10,J,Q,K \right)\text{ }\left( 10,J,Q,K,A \right) \\
\end{align} \right\}\]
There are 10 outcomes in the event N.
