Answer :
The number of different seating arrangements is an illustration of permutation
There are 151200 different seating arrangements
How to determine the number of sitting arrangements
The number of seats (n) is given as:
n = 10
The number of people (r) is given as:
r = 6
So, the number of seating arrangements is:
[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]
This gives
[tex]^{10}P_6 = \frac{10!}{(10 - 6)!}[/tex]
Simplify
[tex]^{10}P_6 = \frac{10!}{4!}[/tex]
Evaluate the quotient
[tex]^{10}P_6 = 151200[/tex]
Hence, there are 151200 different seating arrangements
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