Question

120 pianists compete in a piano competition. (a) In the first round, 30 of the 120 are selected to go on to the next round. How many different outcomes are there for the first round? (b) In the second round, the judges select the first, second, third, fourth and fifth place winners of the competition from among the 30 pianists who advanced to the second round. How many outcomes are there for the second round of the competition?

Answer 1

Explanation:

Given

There are 120 Pianist in a competition

(a)In first round 30 pianist is selected

this can be done in
`^(120)C_(30) ways`

`=(120!)/((120-30)!30!)`

`=(120!)/(90!30!)`

(b)In the second round 5 pianist is selected out of 30

this can be doe by
`=(30!)/((30-5)!5!)`

`=(30!)/(25!5!)`

`=142,506`