More Problems
Probability
Level
3
How many rearrangements of the letters PROBLEMS contains the letters MORE in that order but not necessarily consecutive?
The answer is 1680.
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1 solution
The problem can be viewed in the following way: Lets say we have the letters P,B,L,S and the following structure _ M _ O _ R _ E _. In how many different ways can we arrange our 4 letters in the blank spaces, if there can be more than one letter in each space? The answer to this question is easier to calculate and it is the number of ways to put the letters in the spaces times the number of different arrangements of these 4 letters. The number of different arrangements is 4! =24. The number of ways to place the letters in the spaces is 8C4 =70. Therefore the number of arrangements is 24x70=1680