Three scholarships are available for needy students. Their values are $2,00, $2,400 and $3,000 12 students have applied and no student may receive more than one scholarship. Assuming all 12 students are in need of funds, how many different ways could the scholarship be awarded?

12*11*10

To determine the number of ways the scholarships could be awarded, we can use the concept of combination. Since no student can receive more than one scholarship, we need to calculate the combinations of selecting 3 students from a total of 12.

The formula for calculating combinations is C(n, r) = n! / (r! * (n-r)!), where n is the total number of students and r is the number of scholarships. In this case, n = 12 and r = 3.

Now, let's calculate the number of combinations:

C(12, 3) = 12! / (3! * (12-3)!)
= 12! / (3! * 9!)
= (12 * 11 * 10 * 9!) / (3! * 9!)
= (12 * 11 * 10) / (3 * 2 * 1)
= 220

Therefore, there are 220 different ways the scholarships could be awarded to the 12 students.