Question

Given below are two statements : Statement I: The number of ways to pack six copies of the same book into four identical boxes where a box can contain as many as six books, is 9. Statement II: The minimum number of students needed in a class to guarantee that there are at least six students whose birthday fall in the same month, is 61. In the light of the above statements, choose the correct answer from the options given below.

A.
Both Statement I and Statement II are true
B.
Both Statement I and Statement II are false
C.
Statement I is true but Statement II is false
D.
Statement I is false but Statement II is true

Accepted Answer

A. Statement I: Partition of 6 into at most 4 parts: (6,0,0,0), (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) $ightarrow$ total 9 ways. (True) Statement II: By Pigeonhole Principle, $5 	imes 12 + 1 = 61$ students. (True) Both Statement I and Statement II are true.

Partition of Books and Pigeonhole Principle

Explanation

Practise this under exam conditions