Question

Can someone help figure out how to solve this equation? Thank you!

There 20 people competing in a contest if first place earns $100, second place earns $50 and third place earns $25, How many ways can the three winners be selected?

Answer 1

We will use the binomial coefficient formula to work out the answer

The formula is given by:

`^nC_r= \left(\begin{array}{ccc}n\\r\end{array}\right)= (n!)/((n-r)!r!)`
Where:
'n' is the total population or sample population
'r' is the number of pick

We have:
n = 20
r = 3
Substitute these values into the formula we have

`^(20)C_3= (20!)/((20-3)!3!)=1140`

Answer:
There are 1140 different ways of picking three winners out of 20 people