Question

If the letters of concerned word are arranged as in dictionary, find the rank of the following words: (1)AGAIN (2)INDIA​

Answer 1

Rank of word 'AGAIN' = 27

Rank of word 'INDIA' = 46

Step-by-step explanation:

We are given two words to find out their ranks in dictionary.

(1) AGAIN:

• First the letter 'A' comes.

• We fix 'A' at first position as , A - - - -

• Now, we can see that rest of the four letters can be arranged in $\dfrac{4!}{2!}$ = 12 ways.

• Since, two A's are repeated so, we divide by 2!.

• After 'A', another 'A' comes as; A A - - -

• Now, we can see that three letters G, I, N can be arranged in 3! ways.

• But, in "AGAIN", we are not required A at second position. So we replace the second position by 'G'.

• AG - - -, Now, A, I, N can be arranged in 3! ways.

• By fixing first two positions, we go forward. At the third position, 'A' comes first.

• AGA--, Now I, N can be arranged in one way.

• Thus, we get the rank of word 'AGAIN' = 12 + 6 + 6 + 2 + 1 = 27

(2) INDIA:

• As we have discussed above.

• We can find out the rank of word 'INDIA'.

• A - - - - = $\dfrac{4!}{2!}$= 12 ways

• D - - - - = $\dfrac{4!}{2!}$ = 12 ways

• I A - - - = 3! = 6 ways

• I D - - - = 3! = 6 ways

• I I - - - = 3! = 6 ways

• I N A - - = 2! = 2 ways

• I N D A I = 1 way

• I N D I A = 1  ways

Total ways = 12 + 12 + 6 + 6 + 6 + 2 + 1 + 1 = 46 ways

Thus, the rank of word "INDIA" is 46.