Question

QUESTION Trn drei dubl d ,ac , dne?corsil d t ard Pi n 'respectively Four members of .Och dub-re random ly chosen to partopale n a contest between the two schools. The chosen players of chess Suppose that Jane and her sister Margot are respecfively members of each school aXe)

Answer 1

total number of ways to arrange touranment =N(selecting 3 from each school and then arrrage them for play)

= $\binom{8}{4}\binom{9}{4}*4!$

number of ways Jane and Margot are in team but do not play each other =N(Selecting reaming 3 from 7 of first school and selecting remaing 3 from 8 of second school and then Jane have 3 choices except margot ; next one has reaming 3 choice to play; next 2 choices and last one have 1 choice for competitor)

= $\binom{7}{3}\binom{8}{3}*3*3*2*1$ = $\binom{7}{3}\binom{8}{3}*18$

hence probability = $\binom{7}{3}\binom{8}{3}*18$ / $\binom{8}{4}\binom{9}{4}*4!$