Menu Close

If-the-permutations-of-a-b-c-d-e-taken-all-together-be-written-down-in-alphabetical-order-as-in-dictionary-and-numbered-then-the-rank-of-the-permutation-debac-is-




Question Number 42093 by amansingh@123 last updated on 17/Aug/18
If the permutations of a, b, c, d, e taken  all together be written down in   alphabetical order as in dictionary  and numbered, then the rank of the  permutation  debac  is
$$\mathrm{If}\:\mathrm{the}\:\mathrm{permutations}\:\mathrm{of}\:{a},\:{b},\:{c},\:{d},\:{e}\:\mathrm{taken} \\ $$$$\mathrm{all}\:\mathrm{together}\:\mathrm{be}\:\mathrm{written}\:\mathrm{down}\:\mathrm{in}\: \\ $$$$\mathrm{alphabetical}\:\mathrm{order}\:\mathrm{as}\:\mathrm{in}\:\mathrm{dictionary} \\ $$$$\mathrm{and}\:\mathrm{numbered},\:\mathrm{then}\:\mathrm{the}\:\mathrm{rank}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{permutation}\:\:{debac}\:\:\mathrm{is} \\ $$
Answered by $@ty@m last updated on 17/Aug/18
No. of perm. of letters beginning with a =4!=24  No. of perm. of letters beginning with b =4!=24  No. of perm. of letters beginning with c=4!=24  No. of perm. of letters beginning with da=3!=6  No. of perm. of letters beginning with db=3!=6  No. of perm. of letters beginning with dc=3!=6  No. of perm. of letters beginning with dea=2!=2  ∴ the rank of the perm. debac=  24×3+6×3+2+1=93
$${No}.\:{of}\:{perm}.\:{of}\:{letters}\:{beginning}\:{with}\:{a}\:=\mathrm{4}!=\mathrm{24} \\ $$$${No}.\:{of}\:{perm}.\:{of}\:{letters}\:{beginning}\:{with}\:{b}\:=\mathrm{4}!=\mathrm{24} \\ $$$${No}.\:{of}\:{perm}.\:{of}\:{letters}\:{beginning}\:{with}\:{c}=\mathrm{4}!=\mathrm{24} \\ $$$${No}.\:{of}\:{perm}.\:{of}\:{letters}\:{beginning}\:{with}\:{da}=\mathrm{3}!=\mathrm{6} \\ $$$${No}.\:{of}\:{perm}.\:{of}\:{letters}\:{beginning}\:{with}\:{db}=\mathrm{3}!=\mathrm{6} \\ $$$${No}.\:{of}\:{perm}.\:{of}\:{letters}\:{beginning}\:{with}\:{dc}=\mathrm{3}!=\mathrm{6} \\ $$$${No}.\:{of}\:{perm}.\:{of}\:{letters}\:{beginning}\:{with}\:{dea}=\mathrm{2}!=\mathrm{2} \\ $$$$\therefore\:{the}\:{rank}\:{of}\:{the}\:{perm}.\:{debac}= \\ $$$$\mathrm{24}×\mathrm{3}+\mathrm{6}×\mathrm{3}+\mathrm{2}+\mathrm{1}=\mathrm{93} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *