SOLUTION: How many ways can a class president, vice-president, and secretary be selected from each of the seventh grade and eighth grade to form a six member junior high student council? The

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Question 1149499: How many ways can a class president, vice-president, and secretary be selected from each of the seventh grade and eighth grade to form a six member junior high student council? The seventh grade has 80 members, and the eighth grade has 60 members.
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

7-th grade:  in  N = 80*79*78  ways.


8-th grade:  in  M = 60*59*58  ways.


The united 6-member committee can be formed by N*M ways.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You need P( 80,3 ) and P( 60,3 ) to get all
the possible choices for the 3 offices
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Then you need P( 80,3 ) x P( 60,3 ) to get
all the ways to combine the 7th and 8th
grade choices for the 3 offices
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P( 80,3 ) = +80%21+%2F+%28+80+-+3+%29%21+
P( 80,3 ) = +80%21+%2F+77%21+
P( 80,3 ) = +80%2A79%2A78+=+492960+
and
P( 60,3 ) = +60%21+%2F+57%21+
P( 60,3 ) = +60%2A59%2A58+=+205320+
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P( 80,3 ) x P( 60,3 ) = +492960%2A205320+
P( 80,3 ) x P( 60,3 ) = +101214547200+
101,214,547,200 possible ways
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Definitely get a 2nd opinion on this
( Unless you know what the answer should be )