A fitness magazine surveyed a group of young adults regarding their exercise programs and the following results were obtained.

$4$ were using Program $1,$ Program $2,$ and Program $3$ to improve their fitness.

$7$ were using Program $1$ and Program $2.$

$11$ were using Program $2$ and Program $3.$

$11$ were using Program $1$ and Program $3.$

$15$ were using Program $1$ only.

$26$ were using Program $2.$

$19$ were using Program $3$ but not Program $2.$

$13$ were using something other than these three types of workouts.

Complete parts a through c$.$

a$.$ How many people were surveyed?

people

$($Simplify your answer.$)$

b$.$ How many people were using only Program $2?$

people

$($Simplify your answer.$)$

c$.$ How many people were using Program $3$ but not Program $1?$

people

$($Simplify your answer.$)$