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Question
Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.
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Solution
When expanded, a3 b2 c4 would result in total 9 letters.
This is same as permuting 9 things, of which 3 are similar to the first kind, 2 are similar to the second kind and four are similar to the third kind, i.e. three as , two bs and four cs.
Required number of arrangements =\[\frac{9!}{3!2!4!}\]= 1260
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