Question

If the letters of the word TABLE are permutated in all possible ways and the words thus formed are arranged in the dictionary order(alphabetically), find the ranks of the words
1) TABLE
2) BLEAT

Answer 1

The dictionary order of the letters of given word is $A,B,E,L,T$

In the dictionary order of the words which begin with $A$ come first, If we fill the first place with $A$, remaining $4$ letters $(B,E,L,T)$ can be arranged in $4!$ ways

On preceding like this we get

$\left(i\right)$ The rank of the word $TABLE$

$A----=4!=24$ ways

$B----=4!=24$ ways

$E----=4!=24$ ways

$L----=4!=24$ ways

$TABLE=1$ way

$TABLE=1$ way

Rank of the word $TABLE=4\times 4!+1+1$

$=4\times 24+2$

$=96+2=98$

$\left(ii\right)$ Rank of the word $BLEAT$

$A----=4!=24$ ways

$BA---=3!=6$ ways

$BE---=3!=6$ ways

$BLA--=2!=2$ ways

$BLEAT=1$ ways

Rank of the word $BLEAT=24+6+6+2+1=39$ ways