Arrange It!
Probability
Level
4
Find the number of different ways in which the 10 letters of the word " P R O P O R T I O N " can be arranged if exactly two of the O s are next to each other.
You may use a calculator.
The answer is 70560.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Probability of exactly 2 O s are together
= Probability of [(total ways if no restriction) - (when 3 O s are all separated) - (when 3 O s are together)]
= ( 10P10 / 2P2x2P2x3P3 ) - ( 7P7x8P3 / 2P2x2P2x3P3 ) - ( 3P3x8P8 / 2P2x2P2x3P3 )
= 70560