Aroster for a baseball team has 12 players. the coach is randomly making the batting order for 9 players. what is the probability that you will be the lead-off hitter

The probability of you being the leadoff hitter is 8.3%.

Explanation:

The number of possible rosters can be calculated with permutations, knowing that the coach can choose the first hitter among all 12 players, then the second hitter among the 11 players remaining and so on until the 9th hitter among the remaining 4 players.

Therefore:
Possible rosters = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 = 79833600

The leadoff hitter is the first player in the batting order, therefore the number of possible rosters in which you are chosen as the first one is:
You leadoff = 1 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 = 6652800

The probability of you being leadoff is:
P = You leadoff / Possible rosters 
   = 6652800 / 79833600
   = 1 / 12 
   = 0.08333
   = 8.3%

Note that this is exactly the probability of you being chosen out of the 12 players of the team in a one-pick choice because it does not matter how the rest of the batting order is composed.