(a) 5 ball are identical & 3 boxes are different so no. of ways each box can be filled such that no box remain empty. =‌5−1C3−1=‌4C2=6 option s is correct match. (b) Here balls are different & box are identical. Case-1. 1.1.3 ⇒‌
‌5C1.‌4C1
2!
=10 Case-2. 1.2.2⇒‌
‌5C1.‌4C2
2!
=15 So total no. of ways =25 Option q is correct match. (c) Balls as wall as boxes are identical Case-1 1.1.3 Case-2 1.2.2 So there are two cases only Option p is correct match. (d) ‌35−‌3C125+‌3C21 ‌243−96+3 ‌=150
