Question

Determine whether the scenario below involves permutations or combinations.Ten elementary school students are eligible to be appointed to two positions: plant caretaker and chalkboard assistant. How many unique arrangements of these two positions are possible?

Answer 1

Considering that it matters which position we assign the students, we want *permutations* not combinations

Answer 2

anyways, the answer is \(_{10}P_2=10!/8!=10\times9=90\)

Answer 3

So it's 'Permutation' because the students are applying for a certain job right?

Answer 4

thank you @oldrin.bataku

Answer 5

basically; if we number the students \(0\) to \(9\) and have \((a,b)\) assign student \(a\) to caretaker and student \(b\) to chalkboard assistant. it follows that \((a,b)\) and \((b,a)\) are different since they assign to different positions. these ordered pairs are 2-permutations out of our set of ten student numbers \(\{0,1,2,\dots,9\}\)