Seating rules

In a class are 24 seats but in 7.B class are only 18 students. How many ways can student seat? (The class has 12 benches. A bench is for a pair of students.) Result (large number) logarithm and thus write down as powers of 10.

Result

log n =  20.935

Solution:

n=242322212019181716151413121110987 n=V18(24)=24!(2418)! n=861733891296165888000  logn=20.935 n=1020.935n = 24\cdot 23\cdot 22\cdot 21\cdot 20\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15\cdot 14\cdot 13\cdot 12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7 \ \\ n = V_{ 18 }(24) = \dfrac{ 24! }{ (24-18)! } \ \\ n = 861733891296165888000 \ \\ \ \\ \log n = 20.935 \ \\ n = 10^{ 20.935 }



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