Acompany is placing an order for boxed lunches for a meeting of its executive board. there are 10 members of the board and each will have one lunch. the company is getting the lunches from a restaurant that has 25 varieties of boxed lunches. (a) how many different ways are there for the company to place the lunch order for the 10 lunches? note that it is not important who gets what lunch. all that matters is how many of each of the 25 possible varieties are purchased. (b) how many ways are there for the company to place the lunch order if the 10 lunches purchased are all different? (again, who gets what lunch is not important, just how many of each lunch are purchased).

The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. complete parts (a) and (b) below. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is nothing. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is nothing. (round to three decimal places as needed.)