+0  
 
0
618
2
avatar

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
avatar
0

{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+26364 
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

2 Online Users

avatar