gdk800 wrote:

A firm has 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. (2 groups are considered different if at least one group member is different)

A. 48

B. 100

C. 120

D. 288

E. 600

A general approach to solving Combination problems

Steps:

1. There are two larger groups, the senior partners and the junior partners.

2. The first larger group i.e., the senior partners is 4 in number. So let

n1 be 4. The second larger group, ie, the junior partners is 6 in number. So

n2 is 6.

3. The smaller group that is selected from the larger group of senior partners may be 1, 2, or 3 in number. So

r1 is 1 or 2 or 3 . Correspondingly the other smaller group i.e.,

r2 selected from the junior partners is 2 or 1 or 0 in number.

4. For each value of

r1 and the corresponding

r2, compute the number of combinations which are

4C1 * 6C2,

4C2 * 6C1 and

4C3 * 6C0 being 60, 36 and 4 ways respectively.

5. The total number of combinations is therefore 60+36+4 = 100

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Srinivasan Vaidyaraman

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