Question 1146066
There are 9 "regular" friends and 2 "other" friends. ("Other" friends are friends that cannot both be invited at the same time.)  The woman can invite the following combinations:
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5 regular friends and 0 other friends
4 regular friends and 1 other friend
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Ways to invite 5 regular friends and 0 other friends:
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9C5 = {{{9!/(5!*4!)}}} = 126
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Ways to invite 4 regular friends and 1 other friend:
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9C4 * 2C1 = {{{9!/(4!*5!)}}} * {{{2!/(1!*1!)}}} = 126 * 2 = 252
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So...there are a total of 126 + 252...or 378 ways she can do the invites.