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If the permutations of the first 5 letters, a, b, c, d, e, are arranged in alphabetical order from the beginning to the end, then what is the alphabetical order of the 77th term? How about the 100th term?

Thank you for any help.

 Jul 28, 2018
 #1
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{a, b, c, d, e} | {a, b, c, e, d} | {a, b, d, c, e} | {a, b, d, e, c} | {a, b, e, c, d} | {a, b, e, d, c} | {a, c, b, d, e} | {a, c, b, e, d} | {a, c, d, b, e} | {a, c, d, e, b} | {a, c, e, b, d} | {a, c, e, d, b} | {a, d, b, c, e} | {a, d, b, e, c} | {a, d, c, b, e} | {a, d, c, e, b} | {a, d, e, b, c} | {a, d, e, c, b} | {a, e, b, c, d} | {a, e, b, d, c} | {a, e, c, b, d} | {a, e, c, d, b} | {a, e, d, b, c} | {a, e, d, c, b} | {b, a, c, d, e} | {b, a, c, e, d} | {b, a, d, c, e} | {b, a, d, e, c} | {b, a, e, c, d} | {b, a, e, d, c} | {b, c, a, d, e} | {b, c, a, e, d} | {b, c, d, a, e} | {b, c, d, e, a} | {b, c, e, a, d} | {b, c, e, d, a} | {b, d, a, c, e} | {b, d, a, e, c} | {b, d, c, a, e} | {b, d, c, e, a} | {b, d, e, a, c} | {b, d, e, c, a} | {b, e, a, c, d} | {b, e, a, d, c} | {b, e, c, a, d} | {b, e, c, d, a} | {b, e, d, a, c} | {b, e, d, c, a} | {c, a, b, d, e} | {c, a, b, e, d} | {c, a, d, b, e} | {c, a, d, e, b} | {c, a, e, b, d} | {c, a, e, d, b} | {c, b, a, d, e} | {c, b, a, e, d} | {c, b, d, a, e} | {c, b, d, e, a} | {c, b, e, a, d} | {c, b, e, d, a} | {c, d, a, b, e} | {c, d, a, e, b} | {c, d, b, a, e} | {c, d, b, e, a} | {c, d, e, a, b} | {c, d, e, b, a} | {c, e, a, b, d} | {c, e, a, d, b} | {c, e, b, a, d} | {c, e, b, d, a} | {c, e, d, a, b} | {c, e, d, b, a} | {d, a, b, c, e} | {d, a, b, e, c} | {d, a, c, b, e} | {d, a, c, e, b} | {d, a, e, b, c} | {d, a, e, c, b} | {d, b, a, c, e} | {d, b, a, e, c} | {d, b, c, a, e} | {d, b, c, e, a} | {d, b, e, a, c} | {d, b, e, c, a} | {d, c, a, b, e} | {d, c, a, e, b} | {d, c, b, a, e} | {d, c, b, e, a} | {d, c, e, a, b} | {d, c, e, b, a} | {d, e, a, b, c} | {d, e, a, c, b} | {d, e, b, a, c} | {d, e, b, c, a} | {d, e, c, a, b} | {d, e, c, b, a} | {e, a, b, c, d} | {e, a, b, d, c} | {e, a, c, b, d} | {e, a, c, d, b} | {e, a, d, b, c} | {e, a, d, c, b} | {e, b, a, c, d} | {e, b, a, d, c} | {e, b, c, a, d} | {e, b, c, d, a} | {e, b, d, a, c} | {e, b, d, c, a} | {e, c, a, b, d} | {e, c, a, d, b} | {e, c, b, a, d} | {e, c, b, d, a} | {e, c, d, a, b} | {e, c, d, b, a} | {e, d, a, b, c} | {e, d, a, c, b} | {e, d, b, a, c} | {e, d, b, c, a} | {e, d, c, a, b} | {e, d, c, b, a}

 

The 77th term is =daecb, and the 100th term =eacdb

 Jul 28, 2018
edited by Guest  Jul 28, 2018
 #2
avatar+22896 
0

If the permutations of the first 5 letters, a, b, c, d, e,

are arranged in alphabetical order from the beginning to the end,

then what is the alphabetical order of the 77th term? How about the 100th term?

 

sorted...

\(\begin{array}{|rcll|} \hline 1.& abcde \\ 2.& abced \\ 3.& abdce \\ 4.& abdec \\ 5.& abecd \\ 6.& abedc \\ 7.& acbde \\ 8.& acbed \\ 9.& acdbe \\ 10.& acdeb \\ 11.& acebd \\ 12.& acedb \\ 13.& adbce \\ 14.& adbec \\ 15.& adcbe \\ 16.& adceb \\ 17.& adebc \\ 18.& adecb \\ 19.& aebcd \\ 20.& aebdc \\ 21.& aecbd \\ 22.& aecdb \\ 23.& aedbc \\ 24.& aedcb \\ 25.& bacde \\ 26.& baced \\ 27.& badce \\ 28.& badec \\ 29.& baecd \\ 30.& baedc \\ \hline \end{array} \begin{array}{|rcll|} \hline 31.& bcade \\ 32.& bcaed \\ 33.& bcdae \\ 34.& bcdea \\ 35.& bcead \\ 36.& bceda \\ 37.& bdace \\ 38.& bdaec \\ 39.& bdcae \\ 40.& bdcea \\ 41.& bdeac \\ 42.& bdeca \\ 43.& beacd \\ 44.& beadc \\ 45.& becad \\ 46.& becda \\ 47.& bedac \\ 48.& bedca \\ 49.& cabde \\ 50.& cabed \\ 51.& cadbe \\ 52.& cadeb \\ 53.& caebd \\ 54.& caedb \\ 55.& cbade \\ 56.& cbaed \\ 57.& cbdae \\ 58.& cbdea \\ 59.& cbead \\ 60.& cbeda \\ \hline \end{array} \begin{array}{|rcll|} \hline 61.& cdabe \\ 62.& cdaeb \\ 63.& cdbae \\ 64.& cdbea \\ 65.& cdeab \\ 66.& cdeba \\ 67.& ceabd \\ 68.& ceadb \\ 69.& cebad \\ 70.& cebda \\ 71.& cedab \\ 72.& cedba \\ 73.& dabce \\ 74.& dabec \\ 75.& dacbe \\ 76.& daceb \\ \color{red}77.& \huge{\color{red}daebc} \\ 78.& daecb \\ 79.& dbace \\ 80.& dbaec \\ 81.& dbcae \\ 82.& dbcea \\ 83.& dbeac \\ 84.& dbeca \\ 85.& dcabe \\ 86.& dcaeb \\ 87.& dcbae \\ 88.& dcbea \\ 89.& dceab \\ 90.& dceba \\ \hline \end{array} \begin{array}{|rcll|} \hline 91.& deabc \\ 92.& deacb \\ 93.& debac \\ 94.& debca \\ 95.& decab \\ 96.& decba \\ 97.& eabcd \\ 98.& eabdc \\ 99.& eacbd \\ \color{red}100.& \huge{\color{red}eacdb } \\ 101.& eadbc \\ 102.& eadcb \\ 103.& ebacd \\ 104.& ebadc \\ 105.& ebcad \\ 106.& ebcda \\ 107.& ebdac \\ 108.& ebdca \\ 109.& ecabd \\ 110.& ecadb \\ 111.& ecbad \\ 112.& ecbda \\ 113.& ecdab \\ 114.& ecdba \\ 115.& edabc \\ 116.& edacb \\ 117.& edbac \\ 118.& edbca \\ 119.& edcab \\ 120.& edcba \\ \hline \end{array} % % // ======================================================================= \begin{array}{|rcll|} \hline \hline \end{array} % % // ======================================================================= \begin{array}{|rcll|} \hline \hline \end{array} % % // ======================================================================= \begin{array}{|rcll|} \hline \hline \end{array}\)

 

laugh

 Jul 30, 2018

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