Question 1029765
There are 5 possible ways of drawing 4 hearts, 1 non-heart
HHHHN
HHHNH
HHNHH
HNHHH
NHHHH
Within each of those there are 4 possible positions for the king of hearts so there are 20 (5*4) ways of drawing 4 hearts, one being the king of hearts.
The probability of each outcome is the same,
Let's work it out for KHHHN.
{{{P[1]=(1/52)(12/51)(11/50)(10/49)(38/48)}}}
{{{P[1]=2375/714714}}}
There is one possible way of drawing 5 hearts but then there are 5 positions for the king of hearts.
{{{P[2]=(1/52)(12/51)(11/50)(10/49)(9/48)}}}
{{{P[2]=33/866320}}}
So then putting it all together,
{{{P=20*P[1]+P[2]}}}
{{{P=20(2375/714714)+33/866320}}}
{{{highlight(P=1901089/28588560)}}}