Answer to Question #199113 in Statistics and Probability for mandona

Question

1. Find the number of different ways in which a gold, a silver and a bronze medal can be awarded to 15 competitors if each competitor can win only one medal. 2. In how many different ways may 10 different letters be placed in 15 different boxes, not more than one letter being placed in any box? You may leave the answer in factorial form.

Answer 1

1.) Number of ways to give award to 15 competitors = $^{15}P_3=\dfrac{15!}{12!}=15\cdot14\cdot 13=2730$

2.) For first letter there are 15 options

for second letter , there are 14 options

Similarly, Total number of ways to select 10 different letters = $^{15}P_{10}=\dfrac{15!}{5!}$