Correct Answer - Option 2 : 15120
Solution:
Concept:
To arrange from a list of letters is basically permutation.
Formula:
\({{\rm{n}}_{{{\rm{p}}_{\rm{r}}}}} = \frac{{{\rm{n}}!}}{{\left( {{\rm{n}} - {\rm{r}}} \right)!}}\)
Calculations:
“BEAUTIFUL” has 9 different letters.
Number of possible words \( = {9_{{{\rm{p}}_5}}}\)
⇒ \({9_{{{\rm{p}}_5}}} = \frac{{9!}}{{\left( {9 - 5} \right)!}}\)
⇒ number of possible words = 9 × 8 × 7 × 6 × 5
∴ The number of possible words distinct 5 letter words can be formed from the word “BEAUTIFUL” without repeating the letters is 15120
