Number of ways in which 8 non-identical apples can be distributed among 3 boys such that every boy gets atleast 1 apple and atmost 4 apples.?

Hello student,
There are 3 ways of distributing 8 apples among boys they are
1)4 3 1
2)3 3 2
3)4 2 2
so number of ways= 3!(8c₄)(4c₃)(1c₁)+3(8c₃)(5c₃)(2c₂)+3(8c₄)(4c₂)(2c₂)
=4620