Question

there are 6 people in the ballot for regional judges. voters can vote for any 4. voters can choose to vote for 0,1,2,3,or 4 judges. I'm how many different ways can a person vote?

Answer 1

Answer:

In 517 ways

Step-by-step explanation:

There are total 6 people in ballot and voters can vote for any 4 we have following choices

Voter may not vote for anyone then$^6P_0$

Since, $^nP_r=\frac{n!}{(n-r)!}$  and  $n!=n(n-1)....1$

Here, n=6 and r=0 we will get

$^6P_0=\frac{6!}{(6-0)!}=\frac{6!}{6!}=1$

Voter may not vote for one of them  then  $^6P_1$

$^6P_1=\frac{6!}{(6-1)!}=\frac{6!}{5!}=6$

Voter may not vote for two of them  then  $^6P_2$

$^6P_2=\frac{6!}{(6-2)!}=\frac{6!}{4!}=30$

Voter may not vote for three of them  then  $^6P_3$

$^6P_3=\frac{6!}{(6-3)!}=\frac{6!}{3!}=120$

Voter may not vote for four of them  then  $^6P_4$

$^6P_4=\frac{6!}{(6-4)!}=\frac{6!}{2!}=360$

Total ways in which a person can vote is

$^6P_0$+ $^6P_1$+ $^6P_2$+ $^6P_3$+ $^6P_4$

Substituting the values we will get

[tex]1+6+30+120+360=517[/text]  ways.

Answer 2

Answer:

In 360 different ways can a person vote.

Step-by-step explanation:

Total numbers of vote one can cast = 4

Number of individuals in ballot = 6

Number of distinct ways are there to form the teams for the class:

$P^{n}_{k}=\frac{n!}{(n-k)!}$

where = n = number of elements  = n = 6

k = number of elements choose = 4

$P^{6}_{4}=\frac{6!}{(6-4)!}=360$

In 360 different ways can a person vote.