Given: The word is ‘VOWELS.’
To find : number of words that can be formed using letters of the given word Total number of letters in the word = 6
Formula used : Number of arrangements of n things taken all at a time = P(n, n)
P(n, r) = \(\frac{n!}{(n-r)!}\)
∴ Total number of arrangements
= the number of arrangements of 6 things taken all at a time
= P(6, 6)
= \(\frac{6!}{(6-6)!}\)
= \(\frac{6!}{0!}\)
{∵ 0! = 1}
= 6!
= 6 × 5 × 4 × 3 × 2 × 1
= 720
Hence,
The total number of words can be made by letters of the word ‘VOWELS’ = 720.
