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Algebra
Level
4
If the words, obtained by permuting all the letters C, E, H, K, O, R, S, S, T, T, T, U together, are arranged in correct alphabetic order then what is the alphabetic order (or rank) of the word ‘SHUTTERSTOCK’?
The answer is 21768935.
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1 solution
Using HCR's Formula, rank (R) of any linear permutation is given as follows
R(SHUTTERSTOCK)=6(((11!/3!))/2)+2(((10!/3!))/1)+9(((9!/3!))/1)+6(((8!/2!))/3)+
6(7!/2) +1(6!/1)+ 3(5!/1)+3(4!/1) +3(3!/1)+2(2!/1)+0(1!/1)+1
=19958400+1209600+544320+40320+15120+720+360+72+18+4+0+1= 21768935