Find the number of ways in which 8 non-identical apples can be distributed among 3 boys such that every boy should get at least 1 apple and at most 4 apples.

Explanation

no of ways the apples can be distributed into 3

(1,3,4) ; (2,3,3) ; (2,2,4)

now, applying COMBINATION,

`(3!.^8C_1 * .^7C_3*.^4C_4)+ (3!*.^8C_2*.^6C_3*.^3C_3) + (3!*.^8C_2 * .^6C_2 * .^4C_4)`

`= 3!*((8!7!)/(7!*3!*4!) + (8!*6!)/(2!*6!*3!*3!) + (8!*6!)/(2!*6!*2!*4!)`

`= 3!*(8!)/(3!*4!) + (8!)/(2!*3!*3!) + (8!)/(2!*2!*4!)`