Question

FIND THE NUMBER OF WORDS WITH O MEANING WHICH CAN BE MADE USING ALL LETTERS OF THE WORD FLOWER.IF THESE WORDS ARE TO BE WRITTEN IN DICTIONARY,WHAT IS THE NUMBER OF THE WORD FLOWER.

Answer 1

$$\begin{gathered} \mathrm{FLOWER} \\ \mathrm{Total}\mathrm{no}\mathrm{of}\mathrm{words}\mathrm{which}\mathrm{can}\mathrm{be}\mathrm{made}\mathrm{using}\mathrm{all}\mathrm{the}\mathrm{letters}\mathrm{of}\mathrm{FLOWER}=6!=720 \end{gathered}$$

These letters will be alphabetically arranged as E,F,L,O,R,W
To calculate the rank of word FLOWER in the dictionary, let us follow the sequence shown
Word starting with E : 1* 5! ways
Word starting with F
FE * 4! = 1 * 4! ways
FLE * 3!= 1* 3! ways
FLOE * 2!= 1 *2! ways
FLOR * 2!=1*2! ways
FLOWER=1 ways

Thus Rank of FLOWER = 5! + 4!+3!+2!+2!+1==155