(Sorry not sure if this is basic or university level)

A diner has 16 two-seat booths.

26 guys walk in at random.

what is the probability that at least one booth is empty?

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Is this right:

Total seating arrangements = P( 32, 26) = 3.655 * 10^32

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Arrangements with 3 empty booths = 26! * P( 16, 3 ) = 1.355 * 10^30

Arrangements with 2 empty = P( 28, 26) * P( 16, 2 ) = 3.659 * 10^31

Arrangements with 1 empty = P( 30, 26) * 16 = 1.768 * 10^32

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(seating arrangements with empty booths) / (total seating arrangements)

= ( 2.148 * 10^32 ) / ( 3.655 * 10^32 ) =

**0.588**

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