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

If we need to form a team of 11 students with no left-handed students, we can only choose from the 15 right-handed students. The number of ways to choose 11 students from 15 is:

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

Calculating this gives us 1365.

To find the number of teams containing at least 1 left-handed student, we subtract the number of teams with no left-handed students from the total combinations:

$\text{Teams with at least 1 left-handed student} = C(18, 11) - C(15, 11)$

This equals:

$31824 - 1365 = 30459$

Thus, the number of possible teams containing at least 1 student who is left-handed is 30459.