Solution:
We need to pack 6 indistinguishable books into 4 indistinguishable boxes
The ways we can pack the books are
6,0,0,0 (only one way as 0,6,0,0 or 0,0,6,0 won't be different as boxes are identical)
5,1,0,0
4,2,0,0
4,1,1,0
3,3,0,0
3,2,1,0
3,1,1,1
2,2,2,0
2,2,1,1.
so total 9 ways
Hence statement 1 is correct.
Statement 2
To calculate the minimum number of students required, we need to consider the worst case scenario i.e. the birthdays of students are evenly spread across all the 12 months. We'll have to assume that there are atleast 5 birthday is each month, so the total number of students required =5*12=60. To assure that there is 1 month in which we have 6 birthdays, we'll have to add 1 to this number, hence the minimum number of students required =60+1=61
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