2020 HSC 3U sample questions help (1 Viewer)

[csi]

1. Each of the students in an athletics team is randomly allocated their own locker from a row of 100 lockers. What is the smallest number of students in the team that guarantees that two students are allocated consecutive lockers?

2. A team of 11 students is to be chosen from a group of 18 students. Among the 18 students are 3 students who are left handed. What is the number of possible teams containing at least 1 student who is left handed?

Thanks!

 

[studiesofboard]

The answer to the second question is here: http://www.apexmath.com.au/wp-conte...-HSC-Exam-Mathematics-Extension-1-Answers.pdf

 

[csi]

The answer to the second question is here: http://www.apexmath.com.au/wp-conte...-HSC-Exam-Mathematics-Extension-1-Answers.pdf

thanks

 

[shashysha]

1. Each of the students in an athletics team is randomly allocated their own locker from a row of 100 lockers. What is the smallest number of students in the team that guarantees that two students are allocated consecutive lockers?

2. A team of 11 students is to be chosen from a group of 18 students. Among the 18 students are 3 students who are left handed. What is the number of possible teams containing at least 1 student who is left handed?

Thanks!

First question is use of pigeonhole principle, so its a bit more logical. Let's say no students have consecutive allocated lockers, so that means there's a gap between each locker so you take every second locker. That means theres 50 students in the team. Now if you add 1 student, they're bound to have a consecutive locker with someone else, hence the smallest number is 51.

For the second question, you want to find the amount of groupings with at least 1 left handed, which you can find by doing:
total amount of people - none left handed.
Total would be 18C11 and none left handed would be 15C11 (as theres 3 left handed).
So the answer would be 18C11-15C11 = 30459

 

[csi]

First question is use of pigeonhole principle, so its a bit more logical. Let's say no students have consecutive allocated lockers, so that means there's a gap between each locker so you take every second locker. That means theres 50 students in the team. Now if you add 1 student, they're bound to have a consecutive locker with someone else, hence the smallest number is 51.

For the second question, you want to find the amount of groupings with at least 1 left handed, which you can find by doing:
total amount of people - none left handed.
Total would be 18C11 and none left handed would be 15C11 (as theres 3 left handed).
So the answer would be 18C11-15C11 = 30459

ty