Question

seven runners are competing in a race. in how many ways can the gold silver and bronze medals be awarded?

Answer 1

Now,

Let us consider 3 spaces

i.e

_ _ _

Now,

1st space can be filled in 7 ways

That is gold can be awarded to seven runners in 7 ways

Now,

For 2nd place silver can be awarded in 6 ways

And bronze in 5 ways

So,

Total number of ways in which 3 spaces can be filled is

= 7×6×5

=210

So,

The awards can be given in 210 ways

Answer 2

Number of choices for gold medal = 7 students

Number of choices for silver medal = 6 students (excluding the 1 that has gotten gold)

Number of choices for bronze medal = 5 students (excluding the 2 that have gotten gold and silver )

Total number of ways = 7 x 6 x 5 = 210 ways

Answer: There are 210 ways to award the 3 medals