Question

The number of ways in which $3$ scholarships of unequal value be awarded to $17$ candidates, such that no candidate gets more than one scholarship is

• A. ${}^{17}{C}_3$
• B. ${17}^3$
• C. $3^{17}$
• D. ${}^{17}{P}_3$

Answer 1

The correct option is D ${}^{17}{P}_3$

First scholarship can be given to $17$ students, second scholarship can be given to $16$ students and third scholarship can be given to $15$ students
$\therefore$ Total ways $=17\times 16\times 15={}^{17}{P}_3$