Statement 1: Number of ways in which 30 can bepartitioned into three unequal parts, each part being a natural number is 61.Statement 2; Number of ways of distributing 30identical objects in three different boxes is `^30 C_2dot`

Dear Student

let we will divide 30 into a,b,c inequal partswhen a=1, the number of cases in which we get 30 =13
when a=2, the number of cases in which we get 30 =11
when a=3, the number of cases in which we get 30 =10
when a=4, the number of cases in which we get 30 =8
when a=5, the number of cases in which we get 30 =7
when a=6, the number of cases in which we get 30 =5
when a=7, the number of cases in which we get 30 =4
when a=8, the number of cases in which we get 30 =2
when a=9, the number of cases in which we get 30 =1
Total Number of ways=13+11+10+8+7+5+4+2+1=61
So Assertion is correct
Number of ways of distributing 30 identical objects to 3 boxes =30C3​−1
=30C2​
Reson is correct
So Both Assertion and Reason are correct but reason is not the correct explanation of assertion.



Thanks