Can anyone help me on these? i have no idea how to solve it. Thanks alot!
1)On a soccer team three fullbacks can play any of the three fullback positions, left, center, and right. The three halfbacks can play any of the three halfback positions, the four forwards can play any of the four positions, and the goalkeeper plays only his position. How many different arrangements of the 11 players are possible?
2) From a group of 6 people, 3 are assigned to cleaning, 2 to hauling and one to garbage collecting. How many different ways can this be done?
3) In how many ways can 7 people be made to stand in a straight line? In a circle?
4) A united nations delegation consists of 6 Americans, 5 Russians, and 4 Chinese. Answer the following questions.
a) How many committees of five people are there?
b) How many committees of three people consisting of at least one American are there?
c) How many committees of four people having no Russians are there?
d) How many committees of three people have more Americans than Russians?
e) How many committees of three people do not have all three Americans?
5) To reach his destination, a man is to walk three blocks north and four blocks west. How many different routes are possible?
6) All three players of the women's beach volleyball team, and all three players of the men's beach volleyball team are to line up for a picture with all members of the women's team lined together and all members of men's team lined up together. How many ways can this be done?
7) From a group of 6 Americans, 5 Japanese and 4 German delegates, two Americans, two Japanese and a German are chosen to line up for a photograph. In how many different ways can this be done?
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
Make an attempt to solve these on your own, so we will respond. Consult your text.
Come on, this is your complete set with no thinking. I wlll do two, and you can do the other five and we will check them.
7) ways = 6!/(2!4!) times (5!/(2!4!) times (4!/1!3!)
simplified
ways=5*3*5*2*4= 15*40=600
check that.
On a soccer team three fullbacks can play any of the three fullback positions, left, center, and right. The three halfbacks can play any of the three halfback positions, the four forwards can play any of the four positions, and the goalkeeper plays only his position. How many different arrangements of the 11 players are possible?
1) 3!*3!*4!*1= ...