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(12) distinct prizes are to be distributed among (5) students such that one student receives (4) prizes and each of the remaining (4) students receives (2) prizes. How many distributions are possible?(12) अलग-अलग पुरस्कारों को (5) विद्यार्थियों में बाँटना है, यदि एक विद्यार्थी को (4) पुरस्कार और बाकी (4) विद्यार्थियों को (2)-(2) पुरस्कार मिलें। वितरण के कितने तरीके हैं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (207900)(207900)
Choose the student receiving (4) prizes in (5) ways and distribute as (\frac{12!}{4!(2!)^4}). For distinct objects in fixed group sizes, divide by group factorials.(4) पुरस्कार पाने वाला विद्यार्थी (5) तरीकों से चुनेगा और वितरण (\frac{12!}{4!(2!)^4}) से होगा। वस्तुएँ अलग हों तो समूह-आकारों से भाग दें।
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