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Solutions from a student (dragged) 12

# Solutions from a student (dragged) 12 - Problem 27(counting...

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Problem 27 (counting committees) This is given by the multinomial coe ffi cient 12 3 , 4 , 5 = 27720 Problem 28 (divisions of teachers) If we decide to send n 1 teachers to school one and n 2 teachers to school two, etc. then the total number of unique assignments of ( n 1 , n 2 , n 3 , n 4 ) number of teachers to the four schools is given by 8 n 1 , n 2 , n 3 , n 4 . Since we want the total number of divisions, we must sum this result for all possible combi- nations of n i , or n 1 + n 2 + n 3 + n 4 =8 8 n 1 , n 2 , n 3 , n 4 = (1 + 1 + 1 + 1) 8 = 65536 , possible divisions. If each school must receive two in each school, then we are looking for 8 2 , 2 , 2 , 2 = 8! (2!) 4 = 2520 , orderings. Problem 29 (dividing weight lifters)
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