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

Question

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.

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Answer 1 · 2018-05-30T07:38:36

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

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#