Question 1145629
These are the possible combinations as far as gender is concerned:
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5 men & 1 woman
4 men & 2 women
3 men & 3 women
2 men & 4 women
1 man & 5 woman
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Here are the number of ways each combination can be chosen:
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5 men & 1 woman = 8C5 * 5C1 = {{{(8!/(5!*3!)) * (5!/(1!*4!))}}} = 280
4 men & 2 women = 8C4 * 5C2 = {{{(8!/(4!*4!)) * (5!/(2!*3!))}}} = 700
3 men & 3 women = 8C3 * 5C3 = {{{(8!/(3!*5!)) * (5!/(3!*2!))}}} = 560
2 men & 4 women = 8C2 * 5C4 = {{{(8!/(2!*6!)) * (5!/(4!*1!))}}} = 140
1 man & 5 women = 8C1 * 5C5 = {{{(8!/(1!*7!)) * (5!/(5!*0!))}}} = 8
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Adding these all together...280 + 700 + 560 + 140 + 8...there are <b>1688</b> different ways the team can be chosen.