Complete the following problems: Explain the solution step by step: 1. Suppose t

Question

Complete the following problems: Explain the solution step by step: 1. Suppose that a class contains 15 boys and 25 girls, and that 8 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected 2. Suppose that a class contains 15 boys and 25 girls, and that 8 students are to be selected at random for a special assignment. Find the probability that at least 3 boys and at least 4 girls wil be selected 3. Assume you have 12 books 3 yellow, 4 red and 5 blue and you want to arrange them on a bookshelf. In how many ways can we arrange the books so all red books are at the right side of the shelf? 4. Assume you have 12 books 3 yellow, 4 red and 5 blue and you want to arrange them on a bookshelf. In how many ways can we arrange the books if we want all Blue books on the shelf and we can only fit 10 on the shelf?

Explanation / Answer

Solution:

1) Ways to choose 8 students out of 40 = 40c8 = 40!/(8!*32!) = 76904685

Ways to choose 3 boys out of 15 AND ways to choose 5 girls out of 25
= 15c3 * 25c5 = 15!/(3!*12!) * 25!/(5!*20!)
= 455 * 53130 = 24174150

probability that exactly 3 boys will be selected = 24174150/76904685 = 0.314339107

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