Four identical apples and four identical pears are arranged in a line. How many ways can this be done?

1 Answer
Oct 15, 2017

#(8!)/(4! 4!) = 70#

Explanation:

If we could distinguish the individual fruits then we could arrange them in #8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320# different ways.

For any given arrangement, since we cannot distinguish the individual apples, we need to divide this figure by the number of ways that the apples could be rearranged without us noticing, i.e. #4! = 24# different ways.

Similarly, we need to divide by #4! = 24# for the pears.

That leaves us with:

#(8!)/(4! 4!) = (8*7*6*5)/(4*3*2*1) = 70#

distinguishable arrangements.