Crazy Guests
Eighteen guests have to be seated , half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the seating arrangement can be made. (You may use a calculator ). Enter only the first 6 digits of the number of ways.
DETAILS:
- If number of ways is in the format abcdefgh... , you must enter only first 6 digits , that is, abcdef
The answer is 608370.
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1 solution
Since four particular guests want to sit on a particular side A (say) and three others on the other side B (say). So, we are left with 11 guests out of which we choose 5 for side A in 11C5 ways and the remaining 6 for side B in 6C6 ways. Hence, the number of selections for the two sides is 11C5 x 6C6 .
Now, 9 persons on each side of the table can be arranged among themselves in 9! ways.
Hence, the total number of arrangements = 11C5 x 6C6 x 9! x 9! = 60837035212800
So, our answer is 608370