0 votes 0 votes The number of ways in which 4 boys and 3 girls can be seated in a row such that girls and boys are alternate is :: Answer given by ME is $4!*3! = 144$, but i think $\binom 5 3*4!*3!$ Should be correct. thor asked Jan 7, 2017 thor 597 views answer comment Share Follow See 1 comment See all 1 1 comment reply Uzumaki Naruto commented Jan 7, 2017 reply Follow Share For better clarity, instead of fixing boys(as it says they are alternate), fix the positions of girls as _G_G_G_ which is 3! * 4! 1 votes 1 votes Please log in or register to add a comment.
Best answer 2 votes 2 votes First Boys are arranged in 4! ways now we have 3 positions for girls So, 3C3 B_B_B_B Now girls can be swap their seats therefore 3C3* 3! so total , 3!*4! utk0203 answered Jan 7, 2017 selected Jan 7, 2017 by thor utk0203 comment Share Follow See all 8 Comments See all 8 8 Comments reply thor commented Jan 7, 2017 reply Follow Share Now we have __B__B__B__B__ five positions for Girls. 0 votes 0 votes utk0203 commented Jan 7, 2017 reply Follow Share But if first and last blank are choosen then condition may violate of sitting alternatively.So these are not considered only usable are 3 blanks. 0 votes 0 votes thor commented Jan 7, 2017 reply Follow Share So, my approach gives number of ways such that no two Girls and boys are sitting side by side. rt? 0 votes 0 votes utk0203 commented Jan 7, 2017 reply Follow Share No girls can sit side by side. 0 votes 0 votes thor commented Jan 7, 2017 reply Follow Share it says girls and boys sit alternate 0 votes 0 votes Devwritt commented Jan 7, 2017 reply Follow Share @thor __B1__B2__B3__B4__ five positions for Girls. Ths is wrong approach because if all 3 girls seats in first 3 position , then arrangement will be like: G1 B1 G2 B2 G3 B3 B4 Last two boys violates the condition . So answer is : 3! * 4! = 144 1 votes 1 votes thor commented Jan 8, 2017 reply Follow Share thanx!! 0 votes 0 votes thor commented Jan 8, 2017 reply Follow Share So, can i say The number of ways in which n boys and m girls can be seated in a row such that girls and boys are alternate is $0$ if | n -m | > 1 ? 0 votes 0 votes Please log in or register to add a comment.