Grade 12Algebra
The number of ways of accomodating 7 guests in 3 rooms so thst no room is empty is
a)1260 b)1440 c)1708 d)1806
The number of ways of accomodating 7 guests in 3 rooms so thst no room is empty is
a)1260 b)1440 c)1708 d)1806
1 Answer
Jit Mitra
3^7 - 3*2^7 + 3*1^7 = 2187 - 384 + 3 = 1806
Inclusion-Exclusion principle.
7 guests go into 3 rooms (1 and 2 rooms can be empty) - 7 guests go into 2 rooms (1 and 2 rooms can be empty) + 7 guests go into 1 room (This was excluded twice)
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