Question 1177136: 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?
thank you for helping answer.. :)
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
"ten choose four"; in everyday language, the number of ways of choosing 4 out of 10 objects.
Mathematically....
10 choices for the first number; then 9 for the second, then 8 for the third, and finally 7 for the fourth. That makes 10*9*8*7 = 5040 sequences of four numbers.
But the order the numbers are chosen does not matter -- picking 1, 2, 4, and 7 is the same a picking 4, 2, 7, and 1.
In choosing any particular four of the ten numbers, any one of the four could have been chosen first, any one of the remaining three next, then either of the remaining two, and lastly one way of picking the last. The number of different orders in which any four particular numbers could be chosen is 4*3*2*1 = 24.
So the number of combinations of 4 of the 10 numbers is 5040/24 = 210.
For anyone with experience with this kind of calculation, it is
"10 choose 4" =  =  = 210.
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