There are 12 people in Alice and Bob\'s party and three square tables with 4 sea
ID: 3218646 • Letter: T
Question
There are 12 people in Alice and Bob's party and three square tables with 4 seats each. The first table is white in color, the second table is brown and the third is black. Alice and Bob are figuring out. seating arrangements for their 12 guests. Now recall that for seating arrangements around a table, two seating arrangements are "the same" if one is simply a rotation of another. a. How many different seating arrangements are there for Alice and Bob to consider, assuming it matters who sits in the white table, the brown table and the black table? b. Alice decided that she'll sit in the white table while Bob should sit in the brown table. How many different seating arrangements are there? c. What if Alice and Bob just wants to sit in different tables how many different seating arrangements are there? d. What if Alice and Bob wants to sit in the same table - how many different seating arrangements are there?Explanation / Answer
Number of people = 12
Number of square table = 4 (white brown black)
each table has 4 seats
a)
The number of ways people can sit in a square table is = (4 - 1)! [as we first have to fix one person]
Number of ways of selecting people out of 12 = 12C4
Hence number of ways for first table seating = 12C4 * 3!
Number of ways for second table seating = 8C4 (as 4 people are already on the first table) * 3
Number of ways for third table = 3! (as only 4 people are left)
The different arrangements are = 2970 + 420 + 6 = 3396
b)
Alice in white and bob in brown.
Then the arrangements are = 12C3 * 3! + 8C3 * 3! + 4! = 1320 + 336 + 24 = 1680
c)
In the above combination alice and bob were seating in different table.We just have to find the ways of their seating in different seats.
It will be 3C2 = 3
Hence answer is 3 * 1680
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