All the letters of the word TABLE are permuted and the strings of letters (may or may not have meaning) thus…
All the letters of the word TABLE are permuted and the strings of letters (may or may not have meaning) thus formed are arranged in dietionary order. Then the rank of the word TABLE counted from the rank of the word BLATE is
50
97
61
37
Solution
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 proceeding like this we get
(i) The rank of the word TABLE
\(\begin{aligned}
& \text {A }----=4!=24 \text { ways } \\
& \mathrmB}----=4!=24 \text { ways } \\
& \mathrm{E}----=4!=24 \text { ways } \\
& \mathrm{L}----=4!=24 \text { ways } \\
& \text {TABLE }=1 \text { way } \\
& \text {TABLE }=1 \text { way }
\end{aligned}\)
Rank of the word TABLE \(=4 \times 4!+1+1\)
\(\begin{aligned}
& =4 \times 24+2 \\
& =96+2=98
\end{aligned}\)