$10.$ In a survey conducted on campus, it was found that students like watching the

Barclays Premier League teams: ManU, Chelsea and Arsenal. It was also found that

every student who is a fan of Arsenal is also a fan of ManU or Chlesea $($or both$),$ and $42$

students were fans of ManU, $45$ were fans of Chelsea, $7$ where fans of both ManU and

Chelsea, $11$ were fans of of both ManU and Arsenal, $28$ were fans of both Chelsea and

Arsenal, and twice as many students were fans only of ManU as those who were fans

only of Chelsea.

Find the number of students in the survey who were fans of

$($a$).$ all three football clubs

$($b$).$ Arsenal

$($c$).$ only ManU.$$