Probability of Picking k Winning Numbers in a Lottery

[Punkyc7]

In a lottery , 6 distinct numbers are selected at random from a set {1...50} and designated as a winning number. The player picks six numbers beforehand hoping to include as many numbers as possible. Find the probability that the user picks k winning numbers for k=1,2..,6
So my one concern is that my answers don't sum to 1for K=0 I have (44C6)/(50C6)
for K=1 I have (44C5)/(50C6)
for K=2 I have (44C4)/(50C6)
for K=3 I have (44C3)/(50C6)
for K=4 I have (44C2)/(50C6)
for K=5 I have (44C1)/(50C6)
for K=6 I have (44C0)/(50C6)

My reasoning is that for k=0 you didnt pick any of the six numbers so you must have chosen 6 of the 44 remaining
and used similar reasoning for k=1...6
My question is are my answers right or did i miss something ?

 

[awkward]

Let's consider the case K=2, for example. Let's call your chosen 6 numbers "winners" and the remaining 44 numbers "losers". 44C4 is the number of ways you can pick the 4 losers-- there you are right.

But how many ways are there for you to pick the 2 winners?

 

[Punkyc7]

There are 6C2. So there should be 6C2 * 44C4Thanks that fixed it