Mathematical Statistics one(Counting methods)

Hello, can someone please help me with this question : . . Peter, Dawie and Lebogang are vying for the post of club chairperson in an election to be held next week. The club has a total of 9 ordinary members who will vote in the election. In order for a candidate to be declared winner after the election, he/she needs to have received at least 6 votes in the election otherwise no outright winner will be declared and a rerun will have to be conducted. In how many possible ways may the election result in a winner being declared? . This is how I attempted it. But I got it wrong. . CASE 1(6 votes) I fixed one person to receive 6 votes. While the other 2 can receive 2 and 1 vite This can happen only in 3! ways i.e 621 612 216 261 126 162 Then the remaining 3 votes can be shared in 3^3 ways! . . I followed the same procedure for 7, 8 and 9 votes and ended up with something like . . 6!/6! * 6 * 3^3 + 7!/7! * 3 * 3^2 + 8!/8! * 6 * 3 + 9!/9! * 3 = 210 instead of 2505 . Please help a sister! . Any corrections, suggestions and new methods would be highly appreciated!😘