Question

Ann has 3 oranges and 4 mangoes. Every morning for 7 days she is going to give her brother an orange or a mango. In how many different ways can she do it?

Answer 1

The number of ways is given by:
\[\large \frac{7!}{3!4!}\]
The 7! ways of arranging the fruit have to be divided by 3! and 4!, the reason being that having fixed the positions of the fruit the oranges may be arranged in 3! ways and the mangoes in 4! ways without making a different arrangement.