The different words that can be formed with the letters AAAABBCCD will be 3780.
What is permutation?
The permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.
We have,
AAAABBCCD
i.e.
Total number of letters = 9
Letter A repeated = 4 times
Letter B repeated = 2 times
Letter C repeated = 2 times
Now,
Using the permutation formula,
Permutation (ⁿPr) = n! / r!
So,
Number of ways = 9! / [ 4! × 2! × 2!] = [9 × 8 × 7 × 6 × 5 × 4!] / [ 4! × 2! × 2!] = 3780
Hence we can say that the different words that can be formed with the letters AAAABBCCD will be 3780.
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