Question

if the letters of the word DANGER be permuted in all possible ways and the words forned be arranged as in a dictionary,then the rank of the word GANDER.

Answer 1

hope this will help you... :-)

Answer 2

Answer:

Rank of DANGER is 135

Rank of GARDEN is 379

Rank of GANDER is 373

Step-by-step explanation:

Given:

The given letters are DANGER.  

To find:

To find the rank of GANDER:

Solution:

The given letters in alphabetical order are A D E G N R

(i) GARDEN

The No. of words starting with A (remaining 5 letters) $=5 !=120$

The No. of words starting with D (remaining 5 letters) $=5 !=120$

The No. of words starting with E (remaining 5 letters) $=5 !=120$

The No. of words starting with GAD (remaining 3 letters) $=3 !=6$

The No. of words starting with GAE (remaining 3 letters) $=3 !=6$

The No. of words starting with GAN (remaining 3 letters) $=3 ! =6$

The No. of words starting with GARDEN (remaining 3 letters) $=\frac{1}{3}$

The rank of GARDEN is 379

DANGER

(ii) The No. of words starting with $A=5 !=120$

The No. of words starting with DAE$=3 !=6$

The No. of words starting with DAG$=3 !=6$

The No. of words starting with DANE $=2 !=2$

The No. of words starting with DANGER $=\underline{1=1}$

The rank of DANGER is 135

GANDER

Word starting from $\mathrm{A} \rightarrow 5 !$

Word starting from $\mathrm{D} \rightarrow 5 !$

Word starting from $\mathrm{E} \rightarrow 5 !$

Word starting from GAD $\rightarrow 3 !$

Word starting from GAN $\rightarrow 3 !$

Word starting from GANDER $\rightarrow 1$

Rank $=120+120+120+6+6+1$

Rank $=373$