Q. Sixteen men compete with one another in running swimming and riding. How many prize lists could be made if there were altogether 6 prizes of different values, one for running, 2 for swimming and 3 for riding?
A) $16 \times 15 \times 14$
B) $16^{3} \times 15^{2} \times 14$
C) $16^{3} \times 15 \times 14^{2}$
D) $16^{2} \times 15 \times 14$
Explanation
(b)
Number of ways of giving one prize for running $= 16$
Number of ways of giving one prizes for swimming $= 16 \times 15$
Number of ways of giving three prizes for riding $= 16 \times 15 \times 14$
$\therefore$ Required ways of giving prizes $= 16 \times 16 \times 15 \times 16 \times 15 \times 14$
$= 16^{3} \times 15^{2} \times 14$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.