Question

Problem 1 A dance class consists of 22 students, of which 10 are women and 12 are men. if 5 men and 5 women are to be chosen and then paired off, how many results are possible? Problem 2 A student is to answer 7 out of 10 questions in an examination. How many choices has she? How many if she must answer at least 3 of the first 5 questions? Problem 3 Prove that P(EnFc)-P(E)-P(EnF) Indicate the difference between independent events and mutually exclusive events and give a simple example. . Problem 4 Six balls are to be randomly selected chosen from an urn containing 8 red, 10 green, and 12 blue balls What is the probability at least one red ball is chosen? Given that no red balls are chosen, what is the conditional probability that there are exactly 2 green balls among the 6 chosen? .

Answer 1

dear student please post the question one at a time.

1) Total number of ways to choose 5 men from 12 men is

Total number of ways to select 5 women from 10 men is $_{5}^{10}\textrm{C}=252$

Now 5 men and 5 women can be paired in $5!=120$ ways

Hence total number of results is 120*252*792= 23950080