Question

select the correct answer. 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? 10,800 1,712,304 240 205,476,480

Explanation:

Step1: Use permutation formula

The problem is about choosing 5 students out of 48 for scholarships, and the order of selection matters. The permutation formula is $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 48$ (total number of applications) and $r=5$ (number of scholarships to be awarded).

Step2: Calculate factorial values

$n!=48!$ and $(n - r)!=(48 - 5)!=43!$. So $P(48,5)=\frac{48!}{43!}=\frac{48\times47\times46\times45\times44\times43!}{43!}=48\times47\times46\times45\times44$.

Step3: Perform multiplications

$48\times47 = 2256$, $2256\times46=103776$, $103776\times45 = 4669920$, $4669920\times44=205476480$.

Answer:

205,476,480