A team of 11 students is to be formed from a group of 18 students - HSC - SSCE Mathematics Extension 1 - Question 8 - 2016 - Paper 1

Next, we calculate how many ways we can select 11 students from only the right-handed students. Since there are 15 right-handed students (18 total minus 3 left-handed), we use:

$C(15, 11) = \frac{15!}{11!(15-11)!} = \frac{15!}{11!4!}$

Calculating this gives:

$C(15, 11) = 1365$

To find the number of teams with at least one left-handed student, we subtract the number of teams with no left-handed students from the total number of teams:

$\text{At least 1 left-handed} = C(18, 11) - C(15, 11)$

Substituting the values we calculated:

$\text{At least 1 left-handed} = 31824 - 1365 = 30459$

Thus, the number of possible teams containing at least 1 left-handed student is 30,459.