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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.
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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