Question

answer the questions below. (a) from the 13 albums released by a musician, the recording company wishes to release 9 in a boxed set. how many different boxed sets are possible? (b) 79 athletes are running a race. a gold medal is to be given to the winner, a silver medal is to be given to the second - place finisher, and a bronze medal is to be given to the third - place finisher. assume that there are no ties. in how many possible ways can the 3 medals be distributed?

Explanation:

Step1: Identify combination formula for part (a)

The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 13$ (total albums) and $r=9$ (albums to be selected).
$C(13,9)=C(13,13 - 9)=C(13,4)=\frac{13!}{4!(13 - 4)!}=\frac{13!}{4!9!}$
$=\frac{13\times12\times11\times10\times9!}{4\times3\times2\times1\times9!}=715$

Step2: Identify permutation formula for part (b)

The formula for permutations is $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 79$ (total athletes) and $r = 3$ (number of medal - winning positions).
$P(79,3)=\frac{79!}{(79 - 3)!}=\frac{79!}{76!}=79\times78\times77 =474306$

Answer:

(a) 715
(b) 474306