Question
Question: In how many ways can \(8\) persons be seated on two round tables of capacity \(5\) and \(3\)....
In how many ways can 8 persons be seated on two round tables of capacity 5 and 3.
Solution
To solve this question, we have to do it in 3 steps. In step 1, we have to select 5 out of 8 members to be seated on a big table, then in step 2 arrange the 5 members around the big table and then in step 3 arrange the 3 remaining members on the small table.
Complete step-by-step answer:
Step 1: We have selected 5 out of 8 members to be seated on a big table.
∴No. of ways =8C5
=5!3!8! =5!3×2×18×7×6×5! =56 [ according to law of combination, nCr=r!(n−r)!n!]
Step 2: We arrange 5 selected members around big round table whose capacity is 5 , so no. of ways in which it can be done
∴No. of ways =(5−1)!
=4! =4×3×2×1 =24
Step 3: Now we arrange 3 remaining members around small table whose capacity is 3, so no. of ways it can be arranged is
∴No. of ways =(3−1)!
=2! =2
∴Total no. of ways =56×24×2 =2688.
Hence, 8 person can be seated around a 2 different table in 2688 ways.
Note: Permutation deals with the arrangement of items and combination deals with the selection of items. Order is important in permutations and order is not important in combinations.