Answer:
Explanation:
The number of ways to choose 3 students out of 10 to come in first, second, and third place in a spelling contest, with no ties, is calculated using the combination formula. The combination formula is:
C(n, r) = n! / (r! (n-r)!)
Where n is the total number of items, and r is the number of items to choose. In this case, n = 10 and r = 3.
So, the number of ways to choose 3 students out of 10 is:
C(10, 3) = 10! / (3! (10-3)!) = 10! / (3! 7!) = 10 x 9 x 8 / (3 x 2 x 1) = 120.
Therefore, there are 120 different ways to choose 3 students out of 10 to come in first, second, and third place in a spelling contest, with no ties.