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 general approach to solving Combination problems
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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