Question

For the daily lottery game in Illinois, participants select three numbers between 0 and 9. A number cannot be selected more than once, so a winning ticket could be, say, 307 but not 337. Purchasing one ticket allows you to select one set of numbers. The winning numbers are announced on TV each night. How many different outcomes (three-digit numbers) are possible

Answer 1

120 different outcomes are possible

Explanation:

Since 3 number's are to be selected from a combination of 10 number's without repetition thus number of ways it can be done equals

=
`\binom{10}{3}`

Thus the number of ways are

`(10!)/(3!* 7!)=(10* 9* 8* 7!)/(3* 2* 1* 7!)\\\\=120`