SOLUTION: Using the letters of word {{{GANAPATI}}} how many words can be formed such that all {{{three}}} {{{A}}} come before {{{I}}}

Algebra ->  Permutations -> SOLUTION: Using the letters of word {{{GANAPATI}}} how many words can be formed such that all {{{three}}} {{{A}}} come before {{{I}}}      Log On


   

Question 1172863: Using the letters of word GANAPATI how many words can be formed such that all three A come before I
Answer by greenestamps(13200) About Me  (Show Source):
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By a well known counting principle, the number of distinct arrangements of the letters GANAPATI is

8%21%2F3%21+=+6720

Looking at just the four letters AAAI, the number of distinct ways to arrange them is 4; in only one of them does the I come after all three A's.

So the number of ways of arranging the letters GANAPATI in which all three A's come before the I is

6720%2F4+=+1680