SOLUTION: the number of ways in which a man can invite one or more of his 8 friends to dinner

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Question 773503: the number of ways in which a man can invite one or more of his 8 friends to dinner
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
He can have 1 friend for dinner
He can have 2 friends for dinner
He can have 3 friends for dinner
and so on up to
He can have 8 friends for dinner
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In each of these 8 cases, use the
formula for +C%288%2Cr%29+ where +r+ is
the number of friends invited
to dinner. Note that you don't use
permutations since the order of
the invited friends doesn't matter
----------------------------
So, the solution is:
+C%288%2C1%29+%2B+C%288%2C2%29+%2B+C%288%2C3%29+%2B+C%288%2C4%29+
etc. up to +C%288%2C8%29+
-----------------
+C%288%2C1%29+=+8%21+%2F+%28+1%21%2A%28+8-1+%29%21+%29+
+C%288%2C1%29+=+8%21%2F7%21+
+C%288%2C1%29+=+8+
-----------------
+C%288%2C2%29+=+8%21+%2F+%28+2%21%2A%28+8+-+2+%29%21+%29+
+C%288%2C2%29+=+8%21+%2F+%28+2%2A1%2A6%2A5%2A4%2A3%2A2%2A1+%29
+C%288%2C2%29+=+%28+8%2A7+%29+%2F+2+
+C%288%2C2%29+=+28+
---------------
Continue up to +C%288%2C8%29+ and add up
all the results.