A university research department must select a 4-member committee from a group of 6 biologists and 4 chemists. If the committee must contain at least 1 biologist and at least 1 chemist, how many different 4-member committees can be formed?
Cevap: 194
Cevap
194
Using complementary counting, the total number of ways to pick 4 members out of 10 is 210. The scenarios that break the rule are committees with all biologists (15 ways) or all chemists (1 way). Subtracting these 16 restricted selections from 210 results in 194 valid committees.
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Anahtar Kavram
Combinations with Restrictions (Complementary Counting)