Question

answer the questions below.
? indicate whether its a permutation or a combination.
(5a) a company has 36 employees. a local newspaper is the company asking for a list of the top 5 employees, ranked in order of effectiveness. how many such rankings are possible?

(5b) a company that makes cookies is trying to decide which 5 cookies to include in a promotional mini-box of 8 cookies. the company will choose the 5 mini-box cookies from its collection of 70 cookies. how many mini-boxes are possible?

Explanation:

Step1: Identify permutation for (a)

We need ordered top 3 from 36, use permutation formula $P(n,k)=\frac{n!}{(n-k)!}$
$P(36,3)=\frac{36!}{(36-3)!}=36\times35\times34$

Step2: Calculate permutation value

$36\times35=1260$; $1260\times34=42840$

Step3: Identify combination for (b)

We need unordered 5 from 70, use combination formula $C(n,k)=\frac{n!}{k!(n-k)!}$
$C(70,5)=\frac{70!}{5!(70-5)!}=\frac{70\times69\times68\times67\times66}{5\times4\times3\times2\times1}$

Step4: Calculate combination value

Numerator: $70\times69=4830$; $4830\times68=328440$; $328440\times67=21905480$; $21905480\times66=1445761680$
Denominator: $5\times4\times3\times2\times1=120$
$\frac{1445761680}{120}=12048014$

Answer:

(a) 42840
(b) 12048014