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Do 6 X 6 it equals 36..that's how many

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How many ways can four boys and three girls stand in a line so that no two boys or two girls are next to each other?

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To find the number of ways 3 boys and 2 girls can stand in a row such that the girls are not next to each other, first calculate the total arrangements without restrictions, which is (5!) (for 5 individuals), yielding 120 arrangements. Next, calculate the arrangements where the two girls are together by treating them as a single unit, resulting in (4!) arrangements for the group and (2!) arrangements for the girls within that group, giving (4! \times 2! = 48). Finally, subtract the restricted arrangements from the total: (120 - 48 = 72). Thus, there are 72 ways for the boys and girls to stand so that the girls are not next to each other.


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In how many ways can 3 girls and 5 boys be arranged in a row so that all the 3 girls are together?

6ways. represent boys as<.> girls as</> 1=///..... 2=.///.... 3=..///... 4=...///.. 5=....///. 6=...../// here may be the boys can arranged different ways. 5 boys arranged 5! = 120 ways. In 120 times, each time added girls 6 ways like the above way. so answer is 6*120 = 720 ways we can arrange.


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