Andrinomegamidn
Answered

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

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Sagot :

AGboiiidn

[tex] \large\underline \bold{{SOLUTION}}[/tex]

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

[tex]\longmapsto\rm{P_n= \frac{n!}{(r!)(r!)(r!)(r!)(r!)(r!)(r!)}}[/tex]

[tex]\longmapsto\rm{P_9= \frac{9!}{(1!)(1!)(2!)(1!)(1!)(1!)(2!)}}[/tex]

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

[tex]\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})}}[/tex]

[tex]\longmapsto\rm{P_9=9×8×7×6×5×3×2}[/tex]

[tex]\longmapsto\boxed{\rm{P_9=90,720}}[/tex]

[tex] \large\underline{ \bold{ANSWER}}[/tex]

  • 90 720 distinguishable permutations