The GCF of 30, 48, and 60 is 6.
Answer:
(a) 9 buildings
(b) 2^n -1
Step-by-step explanation:
The number of distinct non-empty subsets of b objects is 2^b -1. Since the subsets are distinct, each could represent a list of the buildings, from the set of b buildings, in which a student is taking courses.
(a) For 8 buildings, 2^8 -1 = 255 students could enroll. for 9 buildings, 2^9-1 = 511 students could enroll.
For 500 students, 9 buildings are required.
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(b) The maximum number of students for n buildings is ...
2^n -1
1+4 = 5
2+5 and add 5 = 12
3+6 and add 12 = 21
4+7+21=32
5+8+32=45
6+9+45=60
7+10+60=77
8+11+77=96
