Letter Arrangement 1
Probability
Level
3
In how many ways can the letters of the word “PHYSICALLY” be arranged such that the L’s are always together but the Y’s aren’t?
The answer is 141120.
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1 solution
In order to satisfy the condition that all the L's are together, we can combine the 2 L's to make 1 "big L". With that, our word becomes "physicaly", which has 9 letters. The number of ways to arrange the Y's such that they won't touch is 7 + 6 + 5 + 4 + 3 + 2 + 1 = 2 8 , and so the number of ways to arrange the other 7 letters is 7 ! , so our answer is 2 8 × 7 ! = 1 4 1 1 2 0