Question

Snow White is bored while the Seven Dwarfs are gone to work for the day, so she takes it upon herself to rearrange the cottage. In how many different orders could she place the Dwarfs' beds?e

Answer 1

We have n choices for the first thing. For each of these n choices, we are left with n-1 choices for the second thing, so that we have n⋅(n−1) choices for the first two things, in order. Now, for each of these first two choices, we have (n-2) choices for the third thing, giving us n(n-1)(n-2) choices for the first three things, in order and so on, until we get down to just two things remaining, and then just one thing remaining. Altogether, n(n-1)(n-2)(n-3)..2.1 ways=n! that we can order n things and that product is just n!( factorial), but with the product written going from n down to 1

Here we have 7 beds. To arrange 7 beds Snow White has 7! ways to arrange them.

Ans)7!=7*6*5*4*3*2*1=5040 ways