A company has 3 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director? Choose the correct choice from the following options.
A) 500 B) 720 C) 4500 D) 25 E) 55
at least one means exactly one and more than one.   different committees with 5 people can be chosen having at least 1 director is   (3c1*5c4) + (3c2*5c3) + (3c3*5c2) = 55;   Hence 55.
<result>E</result>
A company has 3 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director?