subu Posted November 20, 2003 Share Posted November 20, 2003 hi could anybody help me on the following problems in how many ways can 4 girls and 3 boys be arranged in a row so that 1) boys are always together I did this liek this gbbbggg so 5! way and the boys can be arranged in the 3 ppl group in 3! ways so I thought it was 5!*3! ie 720 This answer seems right same logic for the qn below doesnt work 2)boys and girls occupy alternate places g g g g so girls can be arranged in 4! ways and there are 5 spaces so boys can be arranged in 5c3 ways so totally 3!*5c3!4!=1440 ans is 144 2.in how many ways can 6 ppl be arranged in a circle if 2 ppl always 1.together 2.seperated 1.together I did it like this 5!*2! ans is 120 (this one I dont get) 2.seperated I did it like this 4!*2! ans is 48 (this one I get ) Quote Link to comment Share on other sites More sharing options...
dig12us Posted November 20, 2003 Share Posted November 20, 2003 2. The only arrengment could be gbgbgbg so 4 girls can be arrenged in 4! = 24 and 3 boys can be arrenged in 3! = 6 (how did you get 5C3. Its just arrneging 3 boys in a row) total ways 24X6 = 144 Hopefully I am correct Quote Link to comment Share on other sites More sharing options...
sujayath Posted November 21, 2003 Share Posted November 21, 2003 Regarding question 1: 1. Though you got the correct answer 720, it is not because 3! * 5!. Three boys can sit together in 5 patterns ... bbbgggg gbbbggg ggbbbgg gggbbbg ggggbbbb The ways in which boys sit = 3! The ways in which girls sit = 4! So, total ways = 5 * 3! * 4! = 720. Now applying the same logic for the second question ... There is only one way, girls and boys can alternate - gbgbgbg Girls can sit in 4! ways Boys can sit in 3! ways Total ways = 1 * 4! * 3! = 144 I cannot understand the circle question. Could you please eloborate what do you mean by 2 ppl sit together - Is it a particular 2 people, or 3 couples ? Quote Link to comment Share on other sites More sharing options...
dig12us Posted November 21, 2003 Share Posted November 21, 2003 6 people in a circle can be arrenged in 5! = 120 ways. 2 Peple together can be arrenged in 2!(2 people can be arrenged in 2! ways) X 4! (take 2 people as one so total entities will be 5) = 48. In my opinion it cannot be 2!5!. It shoule be 2! (5-1)!. Please correct me if I am wrong 2 People separate should be 5! Quote Link to comment Share on other sites More sharing options...
subu Posted November 21, 2003 Author Share Posted November 21, 2003 hi could anybody help me on the following problems in how many ways can 4 girls and 3 boys be arranged in a row so that 1) boys are always together I did this liek this gbbbggg so 5! way and the boys can be arranged in the 3 ppl group in 3! ways so I thought it was 5!*3! ie 720 This answer seems right same logic for the qn below doesnt work 2)boys and girls occupy alternate places g g g g so girls can be arranged in 4! ways and there are 5 spaces so boys can be arranged in 5c3 ways so totally 3!*5c3!4!=1440 ans is 144 2.in how many ways can 6 ppl be arranged in a circle if 2 ppl always 1.together 2.seperated 1.together I did it like this 5!*2! ans is 120 (this one I dont get) 2.seperated I did it like this 4!*2! ans is 48 (this one I get ) for the first part I think this is fine 4 girls 3 boys if they are to be arranged so that boys are togethere consider the boys as a group ie gggg {bbb} so they can be arranged in 5! ways and hte boys among them selves can be arranged in 3! ways so 5!*3! 2.if teh boys and girls need to alternate u can have it like this bgbgbg g or gbgbgbg or g gbgbgb i thought there are 5 places for the boys to be seated so htey atlernate -g-g-g-g- and we can choose 3 places for 5 boys in 5c3 ways and those boys among themselves can be arranged in 3! ways so I get 5c3*4!*3! 5c3 coz out of 5 places I need to choose 3 please have a look and tellme if I am doing something fundamentally wrong i havent done permutation and combination for years now what books do you refer for it? thanks subu Quote Link to comment Share on other sites More sharing options...
manish2003 Posted November 21, 2003 Share Posted November 21, 2003 Originally posted by dig12us 6 people in a circle can be arrenged in 5! = 120 ways. 2 Peple together can be arrenged in 2!(2 people can be arrenged in 2! ways) X 4! (take 2 people as one so total entities will be 5) = 48. In my opinion it cannot be 2!5!. It shoule be 2! (5-1)!. Please correct me if I am wrong 2 People separate should be 5! I guess we can solve these two scenarios as follows: 1. when two people are together = 48 (as already calculated above) 2. When two people are separate = total number of ways - number of ways in which they are together = 120 - 48 = 72 Any comments? Subu can you verify the answers again? - Manish Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.