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A bag contains 2 white, 3 black, and 5 red objects. In how many ways can three objects be selected if at least one black object must be included?
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Solution: Step 1: Total objects = 2 + 3 + 5 = 10 Step 2: Total ways to select 3 objects = 10 C 3 = 120 Step 3: Ways to select 3 objects without black = 7 C 3 = 35 Step 4: Ways with at least one black = Total ways - Ways without black = 120 - 35 = 85
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