Permutations and Combinations 1 Question 11
11. 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 other on the other side. Determine the number of ways in which the sitting arrangements can be made.
(1991, 4M)
Match the Column
Match the conditions/expressions in Column I with statement in Column II.
Show Answer
Answer:
Correct Answer: 11. $^9 {P}_4 X ^9 {P}_3 (11)!$
Solution:
- Let the two sides be $A$ and $B$. Assume that four particular guests wish to sit on side $A$. Four guests who wish to sit on side $A$ can be accommodated on nine chairs in ${ }^{9} P _4$ ways and three guests who wish to sit on side $B$ can be accommodated in ${ }^{9} P _3$ ways. Now, the remaining guests are left who can sit on 11 chairs on both the sides of the table in (11!) ways. Hence, the total number of ways in which 18 persons can be seated $={ }^{9} P _4 \times{ }^{9} P _3 \times(11)$ !.
