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A question bank has (5) algebra, (4) geometry, and (3) calculation questions. A set of exactly (3) questions must contain at least one algebra and at least one geometry question. How many sets are possible?एक प्रश्न बैंक में (5) बीजगणित, (4) ज्यामिति और (3) गणना प्रश्न हैं। ठीक (3) प्रश्नों का सेट बनाना है जिसमें कम से कम एक बीजगणित और कम से कम एक ज्यामिति प्रश्न हो। कुल सेट कितने हैं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (115)(115)
Count type distributions ((1,1,1)), ((2,1,0)), and ((1,2,0)). Their sum is (5 \times 4 \times 3+\binom{5}{2} \times 4+5 \times \binom{4}{2}).प्रकार-वितरण ((1,1,1)), ((2,1,0)), और ((1,2,0)) गिनें। इनका योग (5 \times 4 \times 3+\binom{5}{2} \times 4+5 \times \binom{4}{2}) है।
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