Question

How many different ways are there to choose the following numbers?

To play the Euromillions lottery you select you select `5` numbers from `1` to `50`. You also select `2` lucky stars from `1` to `11`.
Work out how many different ways are for selecting these `7` numbers. give your answer in standard form correct to `3` significant figures.

Answer 1

`((50),(5))((11),(2))~~117,000,000`

Explanation:

This is a combinations question - we don't care about the order of the picks.

`C_(n,k)=((n),(k))=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

Selecting 5 numbers from 50:

`((50),(5))=(50!)/((45!)(5!))=(50xx49xx48xx47xx46)/120=2,118,760`

Selecting 2 "lucky stars" from 11:

`((11),(2))=55`

We then multiply them together:

`2,118,760xx55=116,531,800~~117,000,000`