How many ways can 3 apples 2 bananas 4 plums and an orange be distributed among 10 children if each child receives one fruit?

Answer 1

To determine the number of ways to distribute 3 apples, 2 bananas, 4 plums, and 1 orange among 10 children, we can use the multinomial coefficient formula. The total number of fruits is 10 (3 apples + 2 bananas + 4 plums + 1 orange). The number of ways to distribute the fruits is given by:

[ \frac{10!}{3! \cdot 2! \cdot 4! \cdot 1!} = \frac{3628800}{6 \cdot 2 \cdot 24 \cdot 1} = 12600. ]

Thus, there are 12,600 ways to distribute the fruits.