select the correct answer. an organization is awarding a $4,000 scholarship to 5 different students. they…

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

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

Answer

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