just wanna know what's the answer to this one.
How many ways can the word "ARRANGED" be arranged so that N and D aren't next to each other?
Thanks. 🙂
[Math] Arranging letters with two letters not next to each other
permutations
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Best Answer
The total number of words is $\binom82\cdot\binom62\cdot\binom41\cdot\binom31\cdot\binom21\cdot\binom11=10080$.
The number of words with ND is $\binom72\cdot\binom52\cdot\binom31\cdot\binom21\cdot\binom11=1260$.
The number of words with DN is $\binom72\cdot\binom52\cdot\binom31\cdot\binom21\cdot\binom11=1260$.
Hence the number of words with no ND and no DN is $10080-1260-1260=7560$.