A firm has 5 senior partners and 7 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)
Answers
A) 145 B) 155 C) 165 D) 175 E) 185
The number of ways to form a group of 3 is 12C3 = 220   The number of groups with no senior partner is 7C3 = 35   The number of groups with at least one senior partner is 220-35= 
<gadget id="calculator">220-35</gadget>
<output>185</output>
185   The answer is 185.
<result>E</result>
A firm has 5 senior partners and 7 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)