Question

An organization is awarding a $ 4,000 scholarship to 5 different students. They have received 48 applications for the scholarships. How many ways can the scholarship winners be chosen? A. 10,800 B. 1,712,304 C. 240 D. 205,476,480

Answer 1

There are 1,712,304 different ways to award the 5 scholarships among the 48 applicants, using the combination formula C(48, 5) which accounts for selections where order does not matter.

Step-by-step explanation:

To determine in how many ways the 5 scholarships can be awarded to students from a pool of 48 applicants, we use the concept of combinations. In mathematics, a combination is a way of selecting items from a collection, where the order of selection does not matter. Since we are selecting 5 students out of 48 and the order of selection does not matter, we use the combination formula:

C(n, k) = n! / (k! * (n - k)!)

Where C(n, k) is the number of combinations, n is the total number of items, and k is the number of items to choose.

For this case:

• n = 48 (total number of students)
• k = 5 (number of scholarships to be awarded)

So, the calculation is:

C(48, 5) = 48! / (5! * (48 - 5)!) = 48! / (5! * 43!)

Calculating this, we get:

C(48, 5) = 1,712,304

The answer is 1,712,304 different ways to award the scholarships.