The Letters Of The Word WOMAN Are Written In All Possible Orders And These Words Are Written Out As In A Dictionary ,then The Rank Of The Word 'WOMAN' Is?

Since all the letters except W come before W so if we fix first position for A then 4 remaining letters can be arranged in 4! Ways and starting with other letters the combinations become 4*4!=96  now comes the words start with W i.e first position is fixed for W  as all the letters come before O so again same fixing A to the first position remaining letters can be arranged in 3! Ways and total combinations become 3*3!=18  same as above the last words can be arranged in 2! Ways fixing A to the third position, it is not 2*2! Because N comes after M  by adding these we get 116 and WOMEN comes on 117  I solve in this way pls tell me if I m wrong.

asnwer is 117

bcos 5!=120

in WOMEN O is second last letter ie it can be 119

but M is between A and N so it can be 117 0r 118

since A is 1st letter so the answer is 117