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There are altogether 19 Chinese visitors and 9 English visitors in a tour. If 5 visitors are selected from the tour to form an activity group consisting of at least 1 Chinese visitor, how many different activity groups can be formed

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理解问题There are altogether 19 Chinese visitors and 9 English visitors in a tour. If 5 visitors are selected from the tour to form an activity group consisting of at least 1 Chinese visitor, how many different activity groups can be formed

已完成理解There are altogether 19 Chinese visitors and 9 English visitors in a tour. If 5 visitors are selected from the tour to form an activity group consisting of at least 1 Chinese visitor, how many different activity groups can be formed

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活动小组组合可能性

  • 组合可能性计算:首先,需要考虑至少有1名中国游客的组合方式。567

中国游客和英国游客的组合

  • 至少1名中国游客:从19名中国游客中选择1名,然后从剩下的27名游客(9名英国游客+剩余的18名中国游客)中选择剩余的4名。组合数为 $ C(19, 1) \times C(27, 4) $。

计算结果

  • 总组合数:计算公式为 $ 19 \times \frac{27 \times 26 \times 25 \times 24}{4 \times 3 \times 2 \times 1} $,得出不同活动小组的组合数。567
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There are altogether 19 Chinese visitors and 9 English visitors in a tour. If 5 visitors are selected from the tour to form an activity group consisting of at least 1 Chinese visitor, how many different activity groups can be formed
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There are altogether 19 Chinese visitors and 9 English visitors in a tour. If 5 visitors are selected from the tour to form an activity group consisting of at least 1 Chinese visitor, how many different activity groups can be formed
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