document.write( "Question 1097044: A certain congressional committee consists of 12 senators and 14 representatives. How many ways can a subcommittee of 5 be formed if at least 4 of the members must be senators? \n" ); document.write( "

Algebra.Com's Answer #711462 by greenestamps(13200) $\"\"$ $\"About$

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The first tutor who responded perhaps misread the problem. His answer is the number of ways that the committee can be formed with EXACTLY 4 senators, which means 1 of the 14 representatives:
\n" ); document.write( " $\"C%2812%2C4%29%2AC%2814%2C1%29+=+495%2A14+=+6930\"$

\n" ); document.write( "But the problem says the committee must have AT LEAST 4 senators. So the earlier answer is missing the number of ways in which all 5 committee members are senators:
\n" ); document.write( " $\"C%2815%2C4%29+=+1365\"$

\n" ); document.write( "So the final answer to the problem is
\n" ); document.write( " $\"6930%2B1365+=+8295\"$ \n" ); document.write( "

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