document.write( "Question 1184938: In how many ways can 3 engineers,4 teachers,4 doctors,3 businessmen and 3 nurses can be seated in a row for COVID 19 check-up so that those of the same carrier sit together?\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #815673 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "In how many ways can 3 engineers,4 teachers,4 doctors,3 businessmen and 3 nurses can be seated
\n" ); document.write( "in a row for COVID 19 check-up so that those of the same carrier sit together?
\n" ); document.write( "~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "We have 5 groups according their professional occupation, and we can permute these 5 groups as whole objects\r\n" );
document.write( "in 5! = 5*4*3*2*1 = 120 ways.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, we can permute by 3! = 6 ways inside the group of 3 engineers;\r\n" );
document.write( "\r\n" );
document.write( "             permute by 4! = 24 ways inside the group of 4 teachers;\r\n" );
document.write( "\r\n" );
document.write( "             permute by 4! = 24 ways inside the group of 4 doctors;\r\n" );
document.write( "\r\n" );
document.write( "             permute by 3! =  6 ways inside the group of 3 businessmen;\r\n" );
document.write( "\r\n" );
document.write( "             permute by 3! =  6 ways inside the group of 4 nurses.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "All these permutations are independent, so the total number of permutations under the imposed condition is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    120*6*24*24*6*6 = 14929920.        ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );