A certain law firm consists of 4 senior partners and 6 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? (Two groups are considered different if at least one group member is different.)
A. 48
B. 100
C. 120
D. 288
E. 600
Groups with AT LEAST 1 senior partner = all possible groups - groups with NO senior partners.
All possible groups:
From 10 partners, the number of ways to choose a group of 3 = 10C3 = (10*9*8)/(3*2*1) = 120.
Groups with no senior partners:
From 6 junior partners, the number of ways to choose a group of 3 = 6C3 = (6*5*4)/(3*2*1) = 20.
Thus:
Groups with at least 1 senior partner = 120-20 = 100.
The correct answer is
B.
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