(a) there are $n$ chairs in a row. find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent. (b) there are 10 chairs in a circle, labelled from 1 to 10. find the number of ways of choosing 3 of these chairs, so that no two chosen chairs are adjacent. (c) there are $n$ chairs in a circle, labelled from 1 to $n.$ find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.

Larissa has also provided the following information. during the year, the company raised $36 million in new long-term debt and retired $20.52 million in long-term debt. the company also sold $22 million in new stock and repurchased $32.4 million. the company purchased $54 million in fixed assets, and sold $6,107,400 in fixed assets. larissa has asked dan to prepare the financial statement of cash flows and the accounting statement of cash flows. she has also asked you to answer the following questions: 1. how would you describe east coast yachts' cash flows? 2. which cash flows statement more accurately describes the cash flows at the company? 3. in light of your previous answers, comment on larissa's expansion plans.

Kumar consulting operates several stock investment portfolios that are used by firms for investment of pension plan assets. last year, one portfolio had a realized return of 12.6 percent and a beta coefficient of 1.15. the average t-bond rate was 7 percent and the realized rate of return on the s& p 500 was 12 percent. what was the portfolio's alpha?

Trade will take place: a. if the maximum that a consumer is willing and able to pay is less than the minimum price the producer is willing and able to accept for a good. b. if the maximum that a consumer is willing and able to pay is greater than the minimum price the producer is willing and able to accept for a good. c. only if the maximum that a consumer is willing and able to pay is equal to the minimum price the producer is willing and able to accept for a good. d. none of the above.