Short Answer TypeHow many 4-digit numbers are there if no digit is repeated?
Or
How many numbers are there between 1000 and 9999 so that no digit is repeated?
The word is 'EQUATION'
Number of letters = 8 (all distinct)
Number of letters to be used = 8
Number of permutations = 
= 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
Additional part:
Fix E in box 1 and N in box 8
Number of permutations for box 1 = 
...(i)
Number of permutations for box 8 = 
...(ii)
Number of letters left = 6 
n = 6
Number of boxes left = 6 
r = 6
∴ Number of permutations = 
...(iii)
From (i), (ii) and (iii), by fundamental principle of counting, the toal number of words formed
= 1 x 1 x 720 = 720.
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that no two consonants are together.
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