Question

In a running competition, a bronze, silver and gold medal must begiven to the top three girls and top three boys. If 11 boys and 12 girlsare competing, how many different ways could the six medals possiblybe given out?

Answer 1

We have to find how many ways these 6 medals can be given.

We start with the boys.

We have 11 candidates for the gold medal.

After selecting one for the gold medal, we have 10 options for the silver medal. This is 10 options for each of the 11 options for the gold medal.

In the same way, we have 9 options for the bronze medal.

Then, if we multiply we get the possible arrangements:

`n_b=11\cdot10\cdot9=990`

For the girls, we can repeat the process but by starting with 12 options for the gold medal, 11 options for the silver medal and 10 options for the bronze medal:

`n_g=12\cdot11\cdot10=1320`

The total possible arrangements is the multiplication of the arrangements for the boys and the arrangements for the girls:

`N=n_b\cdot n_g=990\cdot1320=1306800`

Answer: 1,306,800 ways