Question

A game in a state lottery selects four numbers from a set of numbers,{0,1,2,3,4,5,6,7,8,9} with no number being repeated. how many possible groups of four numbers are possible?

Answer 1

We need to select four numbers out of ten without repetition.

Thus for the 1st place there are 10 possible numbers, 9 for the 2nd place, 8 for the 3rd and 7 for the 4th, therefore we have:

$10\cdot9\cdot8\cdot7=5040$ possible outcomes,

Or

n = 10

m = 4

$P(n,m)=\frac{n!}{(n-m)!}=\frac{10!}{6!}=5040$

Answer: 5040