Question

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

• A. ${}^{17}{P}_1$
• B. ${}^{17}{P}_{17}$
• C. ${}^{17}{P}_3$
• D. None of these

Answer 1

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

There are $3$ scholarships to be awarded between $17$ candidates $\xi$ no one candidate can get more than one scholarship.

The $1st$ scholarship can be given to any of the $17$ candidates, So $17$ choices.

$\Rightarrow$ The $2nd$ can be given to the remaining $16$ candidates in ${}^{16}{C}_1=16$ ways.

Similarly the third in $15$ ways.

$\Rightarrow$ Total $=17\times 16\times 15={}^{17}{P}_3$

Hence, the answer is ${}^{17}{P}_3.$