ABC's
Probability
Level
4
Find the number of arrangements of the letters AAAABBBC in which either the A's appear together in a block of four letters or the B's appear together in a block of three letters.
The answer is 44.
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1 solution
The number of arrangements with 4 A's together is 3 ! 5 ! = 2 0 .
The number of arrangements with 3 B's together is 4 ! 6 ! = 3 0 .
The number of arrangements with 4 A's together and 3 B's together is 3 ! = 6 .
Thus the total number of arrangements as per the requirements is 2 0 + 3 0 − 6 = 4 4 .