Respuesta :
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[tex]^6P_0[/tex]
Since, [tex]^nP_r=\frac{n!}{(n-r)!}[/tex] and [tex]n!=n(n-1)....1[/tex]
Here, n=6 and r=0 we will get
[tex]^6P_0=\frac{6!}{(6-0)!}=\frac{6!}{6!}=1[/tex]
Voter may not vote for one of them then [tex]^6P_1[/tex]
[tex]^6P_1=\frac{6!}{(6-1)!}=\frac{6!}{5!}=6[/tex]
Voter may not vote for two of them then [tex]^6P_2[/tex]
[tex]^6P_2=\frac{6!}{(6-2)!}=\frac{6!}{4!}=30[/tex]
Voter may not vote for three of them then [tex]^6P_3[/tex]
[tex]^6P_3=\frac{6!}{(6-3)!}=\frac{6!}{3!}=120[/tex]
Voter may not vote for four of them then [tex]^6P_4[/tex]
[tex]^6P_4=\frac{6!}{(6-4)!}=\frac{6!}{2!}=360[/tex]
Total ways in which a person can vote is
[tex]^6P_0[/tex]+ [tex]^6P_1[/tex]+ [tex]^6P_2[/tex]+ [tex]^6P_3[/tex]+ [tex]^6P_4[/tex]
Substituting the values we will get
[tex]1+6+30+120+360=517[/text] ways.
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:
[tex]P^{n}_{k}=\frac{n!}{(n-k)!}[/tex]
where = n = number of elements = n = 6
k = number of elements choose = 4
[tex]P^{6}_{4}=\frac{6!}{(6-4)!}=360[/tex]
In 360 different ways can a person vote.
