+556 My grandpa has 10 pieces of art, including 3 prints by Escher. If he hangs the pieces of art in a row in a random order, what is the probability that all three pieces by Escher will be placed consecutively?
+129630 Total arrangements possible = 10!
Arrangements where the three prints are together =
They can occupy any of 8 positions...and for each of these, they can be arranged in 3! ways.....and the other prints can be arranged in 7! ways......so we have
8 * 3! * 7 !
So....the total probability is :
[ 8 * 3! * 7! ] / 10! = [8 * 6] / [10 * 9 * 8 ] = 6 / 90 = 1 / 15
+129630 Total arrangements possible = 10!
Arrangements where the three prints are together =
They can occupy any of 8 positions...and for each of these, they can be arranged in 3! ways.....and the other prints can be arranged in 7! ways......so we have
8 * 3! * 7 !
So....the total probability is :
[ 8 * 3! * 7! ] / 10! = [8 * 6] / [10 * 9 * 8 ] = 6 / 90 = 1 / 15
