a)In how many ways can 5 boys and 5 girls stand in a row if noboy is beside anot

Question

a)In how many ways can 5 boys and 5 girls stand in a row if noboy is beside another boy and no girl is beside another girl? b) If you removed the restriction from part a) that no girl isbeside another girl but kept the restriction that no two boyscan be beside one another, in how many ways could the 10 childrenstand in a row? a)In how many ways can 5 boys and 5 girls stand in a row if noboy is beside another boy and no girl is beside another girl? b) If you removed the restriction from part a) that no girl isbeside another girl but kept the restriction that no two boyscan be beside one another, in how many ways could the 10 childrenstand in a row?

Explanation / Answer

a) There are two sequences that apply: XOXOXOXOXO   and OXOXOXOXOX. There are 5! possibilities for theboys and 5! possibilities for the girls. Putting it togetherwe get:    2 * 5! * 5! = 28800 possibilities. b) Beyond the two sequences above we now also have: XOOXOXOXOX, XOXOOXOXOX, XOXOXOOXOX, XOXOXOXOOX. This brings our sequences to 6. So now we have 6 * 5! * 5! = 86400. Hope this helps!

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