Question

how many ways can I arrange 5 chairs, 2 at a time?

Answer 1

This is a problem of permutation, since position of selected chairs is also taken into the consideration

(for example interchanging position of selected chairs 4 and 5, from position 1 and 2 to position 2 and 1 respectively, gives us one more way to arrange the chairs

We have 5 choices of chairs, and we have to arrange 2 of them at a time, so we have 2 positions to place 2 chairs out of 5

n = 5,

r = 2

Number of ways we can arrange 5 chairs, 2 at a time

=⁵P₂

= n! / r!

= 5! / 2!

= 60