Step 1: Write all the alphabets in alphabetical order.
ACHIN Step 2 : Give a number to each alphabet starting from 0 in alphabetical order.
Step 3: In Word "SACHIN" first alphabet is 'S' which is present in the
5‌th ‌ position in the Alphabet Box. And after 'S', in the word "SACHIN" there are 5 alphabets "ACHIN" which we can arrange in 5 ! Ways.
So for Alphabet '
S ' we write
5×5 !
Step 4 : As in word "SACHIN" we calculated 'S', so delete 'S' from Alphabet box and check remaining alphabets got right numbers or not in Alphabet box.
Step 5: Now next alphabet after '
S ' in word "SACHIN" is '
A ' which is present in the
0‌th ‌ position in the New Alphabet Box. And after '
A ' in the word "SACHIN"
there are 4 alphabets "
CHIN " which we can arrange in 4 ! Ways.
So for Alphabet '
A ' we write
0×4 !
Step 6: Now as in word "SACHIN" we calculated 'A', so delete 'A' from Alphabet box and check remaining alphabets got right numbers or not in Alphabet box. As you can see after deleting '
A '
O‌th ‌ position in the Alphabet box is missing so we have to create a new alphabet table.
Step 7 : Now next alphabet after '
A ' in word "SACHIN" is '
C ' which is present in the
0‌th ‌ position in the New Alphabet Box. And after '
C ' in the word "SACHIN" there are 3 alphabets "HIN" which we can arrange in 3 ! Ways.
So for Alphabet '
C ' we write
0×3 !
Step 8: Now as in word "SACHIN" we calculated '
C ', so delete '
C ' from Alphabet box and check remaining alphabets got right numbers or not in Alphabet box. As you can see after deleting '
C '
0‌th ‌ position in the Alphabet box is missing so we have to create a new alphabet table..
Step 9 : Now next alphabet after '
C ' in word "SACHIN" is '
H ' which is present in the
0‌th ‌ position in the New Alphabet Box. And after '
H ' in the word "SACHIN"
there are 2 alphabets "IN" which we can arrange in 2 ! Ways.
So for Alphabet '
H ' we write
0×2 !
Step 10: Now as in word "SACHIN" we calculated '
H ', so delete '
H ' from Alphabet box and check remaining alphabets got right numbers or not in Alphabet box. As you can see after deleting '
H '
O‌th ‌ position in the Alphabet box is missing so we have to create a new alphabet table.
Step 11: Now next alphabet after '
H ' in word "SACHIN" is '
I ' which is present in the
0‌th ‌ position in the New Alphabet Box. And after '
l ' in the word "SACHIN"
there are 1 alphabets "
N " which we can arrange in 2 ! Ways.
So for Alphabet ' 1 ' we write
0×1 !
Step 12 : Now as in word "SACHIN" we calculated ' 1 ', so delete '
I ' from Alphabet box and check remaining alphabets got right numbers or not in Alphabet box. As you can see after deleting '
l '
0‌th ‌ position in the Alphabet box is missing so we have to create a new alphabet table.
Step 13 : Now next alphabet after ' 'l' in word "SACHIN" is '
N ' which is present in the
0‌th ‌ position in the New Alphabet Box. And after '
N ' in the word "SACHIN"
there are no alphabet so it is the last alphabet.
So for last Alphabet '
N ' we always write 0 !
Position of the word 'SACHIN' in the dictionary
‌=5×5!+0×4!+0×3!+0×2!+0×1!+0!‌=600+1‌=601