The probability of you being the leadoff hitter is <span>8.3%.</span>
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 <span>× 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 = 6652800
The probability of you being leadoff is:
P</span> = You leadoff / <span>Possible rosters
</span> = 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.
For the five characters of the five-character password, the first three slots are already taken for the initial F, J, S, the password would become,
FJS_ _
The last two slots could be any of the even digits. In the fourth slot, Fiona can have any of the 5 values. On the fifth slot, she can have only 4 choices as the other digit was already used. Multiplying 5 and 4, the answer would be 20.
You problem is you don't have any problem. You have a bunch of formulas for the perimeter and area of some shapes.
As for using the formulas, usually you're given all but one of the variables and you can solve for the remaining one.
Notice how the triangle result doesn't have area as a function of a, b and c. That's called Heron's formula and is usually not taught to secondary school students. I don't like to teach it either because Archimedes' Theorem is so much better:
The sides a,b,c and area S of a triangle satisfy
The coordinates of the school is now (5,7).
