В студентській групі навчається 13 хлопців і 7 дівчат. Навмання вибирають 5
студентів. Знайдіть ймовірність того, що серед відібраних буде:
а) тільки 3 хлопці;
б) хоча б одна дівчина.
1.10 Сім підручників і три задачника випадковим чином розташовані на
полиці.
Знайдіть імовірність того, що:
а) задачники будуть розташовані поряд;
б) між задачниками виявиться два підручника.
The beardless sly man Aldar-Kose lived in one aul. His eyes were sharp, his legs were quick, his hands were agile, and his mind was even more agile. Aldar-Kose loved to joke and laugh, especially at fools and misers. He had no wealth, but by cunning he did not get himself a meal of fat ram.
Zhatyr-bai was a greedy and stupid person. His flocks were large: he would start counting at dawn, and finish at dusk. Once Aldar-Kose came to him and said:
- Honorable buy, I have two rubles, but no wallet. I walk, hold the money in my hand - my hand is tired. I want to get rid of this money. Will you help me?
- Come on, come on, I will help! - buy was delighted. - Just tell me how?
“Sell me some poor little goat for two rubles,” says Aldar-Kose.
Thought, thought buy: "Well, you can sell." He caught a lame goat in the herd, skinny, barely alive, which had only two days left to die, and gave to Aldar-Kose:
- Here, take it, although it's a pity to give it away cheaply. Good kid. Give me two rubles!
Aldar-Kose took a goat, and keeps money in his fist:
- You know what, honorable buy. I changed my mind. Take two rubles and a kid to boot, and give me a lamb.
“Well, not a bad exchange,” thought Bay, “two rubles and even a kid to boot!” - and went to catch the lamb. Caught the smallest and serves Aldar-Kose:
- Here, take it. Nice lamb. Give me two rubles and a kid.
Aldar-Kose took the lamb, but he holds the money in his fist and does not let go of the goat:
- You know what, honorable buy. I changed my mind. Take two rubles, a kid and a lamb to boot, and give me a goat.
"Not a bad exchange," thought Bay, "two rubles and a goat, and even a lamb to boot." And he went to catch a goat. He caught the thinnest one and serves to Aldar-Kose:
- Here, take it, good goat. Give me two rubles, a kid and a lamb.
- Wait, wait, respectable bay! - says Aldar-Kose. - I changed my mind. Take two rubles, a kid, a lamb and a goat in addition, and give me only one ram, but let me choose it myself.
“This exchange is more profitable than all the others! - thought the delighted buy. - Two rubles, a kid, a lamb and even a goat to boot - and all this for one ram! And he says to Aldar-Kose:
- Well, choose!
He chose Aldar-Kose for himself the biggest, fatty ram, gave the bai two rubles, a kid, a lamb and a goat in addition, put the ram on his shoulders and went, and bai Zhatyr-bai laughed, rubbing his hands:
- What a fool Aldar-Kose! He gave so much good for just one ram!
Bay did not understand which of them was the fool.
82 км/ч и 76 км/ч
Пошаговое объяснение:
Если бы скорости поездов были одинаковы, то поезда встретились бы на середине расстояния между городами, т.е. каждый бы до момента встречи (через 10 ч):
s=1580:2=790 км.
Но т.к. скорость одного поезда на 6 км/ч больше, чем другого, то за 10 часов этот поезд на 6 км/ч*10 ч=60 км больше, чем второй. Точка встречи поездов смещена от середины пути на вот эти 60 км. Половину этих 60 км - 30 км "быстрый" поезд, и половину "недошел" другой, более медленный.
Т.о. первый поезд ("быстрый" до места встречи расстояние:
s₁=790 км + 60:2 км = 790+30=820 км,
второй поезд ("медленный" до места встречи расстояние
s₂=790 км - 60:2 км = 790-30=760 км.
А, т.к. оба расстояния пройдены за одинаковое время 10 ч, то скорости:
v₁=820:10=82 км/ч
v₂=760:10=76 км/ч