Find the number of permutations of the letters of the word HAPPINESS.. Created by andrinomegam. Math

Let n be the total of the letters , and r be the times the repeated letters are.90 720 distinguishable permutations

Find the number of permutations of the letters of the word HAPPINESS....

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andrinomegam @andrinomegam

October 2022 1 1 Report

Find the number of permutations of the letters of the word HAPPINESS.

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AGboii

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$\large\underline \bold{{SOLUTION}}$

Let n be the total of the letters , and r be the times the repeated letters are.

$\longmapsto\rm{P_n= \frac{n!}{(r!)(r!)(r!)(r!)(r!)(r!)(r!)}}$

$\longmapsto\rm{P_9= \frac{9!}{(1!)(1!)(2!)(1!)(1!)(1!)(2!)}}$

$\longmapsto\rm{P_9= \frac{9×8×7×6×5×4×3×2×1}{(1)(1)(2×1)(1)(1)(1)(2×1)}}$

$\longmapsto\rm{P_9= \frac{9×8×7×6×5×\cancel{4}×3×2×1}{(\cancel{1)(1)(2×1)(1)(1)(1)(2×1})}}$

$\longmapsto\rm{P_9=9×8×7×6×5×3×2}$

$\longmapsto\boxed{\rm{P_9=90,720}}$

$\large\underline{ \bold{ANSWER}}$

90 720 distinguishable permutations

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