Navbatda Uchta Odam 8Ad687
1. Masala: A va B orasida uchta odam bo'lish ehtimolini topish.
2. Berilgan: A va B navbatda turibdi, ular orasida yana 8 odam bor, jami 10 odam.
3. Masala sharti: A va B orasida aniq 3 odam bo'lishi kerak.
4. Bu kombinatorik masala, ya'ni 8 odam orasidan 3 tasini tanlash ehtimoli:
$$ P = \frac{\binom{8}{3}}{\binom{10}{3}} $$
5. Hisoblaymiz:
$$ \binom{8}{3} = \frac{8!}{3!5!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56 $$
$$ \binom{10}{3} = \frac{10!}{3!7!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 $$
6. Shunday qilib, ehtimol:
$$ P = \frac{56}{120} = \frac{7}{15} \approx 0.4667 $$
Javob: A va B orasida uchta odam bo'lish ehtimoli $\frac{7}{15}$ yoki taxminan 0.467.