The Lagrangian is
with partial derivatives (set equal to 0)
Case 1: If 
, then
Then
So we have two critical points, 
and 
Case 2: If 
, then in the first equation we get
and from the third equation,
Then
but there are no real solutions for 
, so this case yields no additional critical points.
So at the two critical points we've found, we get extreme values of
(min)
and
(max)
No, because 60*3=180/20=9*.24=2.16
The amount the bottle can hold is 1.5 liters and 1.5<2.16
The quick way to get the answer is just type "42 choose 11" into Google.
Or if you want to figure it out yourself, you have 42 choices for the first potential juror, 41 choices for the second potential juror, etc.
Now before you stop there, you only care about the combination of the 11 people chosen, not what order they are selected, so you need to divide by the ways to arrange 11 people.
Final expression:
C(42,11) = (42 * 41 * 40 * 39 * 38 * 37 * 36 * 35 * 34 * 33 * 32) / (11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
Answers:
4,280,561,376 ways
2.4•10^-10
the dot is the multiplication symbol and the -10 is the exponent
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