1. A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
2.Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month,2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
3. This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?
The number of combinations are equal to
2*Combination with 3 in first office + Combination with 2 in first office + Combination with 1 in first office
= 2*1 + 3C2 + 3C2 = 8
Total number of hours = x/3*7/5 + 2x/3 = 17x/15
Fraction for deluxe = (7x/15) / (17x/15) = 7/17
Let '1' be total income this year and x be the saved money
Income spent = 1-x
Income saved = x
(r+1)x = (1-x)/2
2rx+2x = 1-x
x = 1/(2r+3)