Question

• (A) Distribute 4 fruits (1 apple, 1 orange, 1 banana, 1 peach) to 6 children, no child gets more than 1 piece
• (B) Distribute 4 oranges to 6 children, no child gets more than 1 orange
• (C) Distribute 4 fruits (1 apple, 1 orange, 1 banana, 1 peach) to 3 children, a child may get more than 1 piece
• (D) Distribute 4 oranges to 3 children, a child may get more than 1 orange

Answer 1

(A) 4 fruits can be distributed to 6 children in = 6*5*4*3 ways = 360

(B) here all the fruits are same , that is oranges , so they can be distributed in = 6C4 ways = 360/4! = 15 ways

(C) first choose 3 fruits out of 4, distribute them one to each. Now give rhe remaining one to any of the remaining = 4 * (3 * 2 *1) * 4 = 96

(D) here order of fruits doesn't matter, as they are all same.

All would get same oranges except one getting 2.

There are three children so there are three options for having 2 oranges to one of the child

Thus number of ways = 3