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](https://tex.z-dn.net/?f=%5E6P_0)
Since,
and ![n!=n(n-1)....1](https://tex.z-dn.net/?f=n%21%3Dn%28n-1%29....1)
Here, n=6 and r=0 we will get
![^6P_0=\frac{6!}{(6-0)!}=\frac{6!}{6!}=1](https://tex.z-dn.net/?f=%5E6P_0%3D%5Cfrac%7B6%21%7D%7B%286-0%29%21%7D%3D%5Cfrac%7B6%21%7D%7B6%21%7D%3D1)
Voter may not vote for one of them then ![^6P_1](https://tex.z-dn.net/?f=%5E6P_1)
![^6P_1=\frac{6!}{(6-1)!}=\frac{6!}{5!}=6](https://tex.z-dn.net/?f=%5E6P_1%3D%5Cfrac%7B6%21%7D%7B%286-1%29%21%7D%3D%5Cfrac%7B6%21%7D%7B5%21%7D%3D6)
Voter may not vote for two of them then ![^6P_2](https://tex.z-dn.net/?f=%5E6P_2)
![^6P_2=\frac{6!}{(6-2)!}=\frac{6!}{4!}=30](https://tex.z-dn.net/?f=%5E6P_2%3D%5Cfrac%7B6%21%7D%7B%286-2%29%21%7D%3D%5Cfrac%7B6%21%7D%7B4%21%7D%3D30)
Voter may not vote for three of them then ![^6P_3](https://tex.z-dn.net/?f=%5E6P_3)
![^6P_3=\frac{6!}{(6-3)!}=\frac{6!}{3!}=120](https://tex.z-dn.net/?f=%5E6P_3%3D%5Cfrac%7B6%21%7D%7B%286-3%29%21%7D%3D%5Cfrac%7B6%21%7D%7B3%21%7D%3D120)
Voter may not vote for four of them then ![^6P_4](https://tex.z-dn.net/?f=%5E6P_4)
![^6P_4=\frac{6!}{(6-4)!}=\frac{6!}{2!}=360](https://tex.z-dn.net/?f=%5E6P_4%3D%5Cfrac%7B6%21%7D%7B%286-4%29%21%7D%3D%5Cfrac%7B6%21%7D%7B2%21%7D%3D360)
Total ways in which a person can vote is
+
+
+
+ ![^6P_4](https://tex.z-dn.net/?f=%5E6P_4)
Substituting the values we will get
[tex]1+6+30+120+360=517[/text] ways.