Question

The number of ways of 3 scholarship 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 ${}^{17}{P}_3$

There are $3$ scholarships to be awarded between $17$ candidates so that 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 ${}^{17}{P}_3$