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The number of different seating arrangements is an illustration of permutation
There are 151200 different seating 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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