Question

12 persons are to be arranged around two round table such that one table can accommodate seven persons and another five persons only.

Number of ways of arrangement if 2 particular persons A and B do not want to be on the same table is

• A. ${}^{10}{C}_{4}6!4!$
• B. ${2.}^{10}{C}_{6}6!4!$
• C. ${}^{11}{C}_{6}6!4!$
• D. ${2.}^{11}{C}_{6}6!4!$

Answer 1

The correct option is B ${2.}^{10}{C}_{6}6!4!$

A can sit on first table and B on the second or A on the second and B on the first table
If A is on the first table, then remaining six for first table can be selected in ${}^{10}{C}_6$ ways.
Now these 7 persons can be arranged in 6! Ways remaining 5 can be arranged in 4! Ways.
Hence, total number of ways is = ${2.}^{10}{C}_{6}6!4!$