anonymous one year ago You have 7 balls that are each a different color of the rainbow. In how many distinct ways can these balls be ordered?

• This Question is Open
1. anonymous

1 7 49 343 5,040

2. ybarrap

Start easy. If you had one ball, how many ways can you order it?

3. anonymous

looks like @ybarrap has this one!

4. anonymous

5. anonymous

each of the seven balls is distinct; there are $$7!$$ such ways of arranging them since there are $$7$$ possibilities for the first ball of the order, the other $$6$$ for the second, the remaining $$5$$ for the third, then $$4$$, $$3$$, $$2$$, and ultimately $$1$$ for the final position -- so $$7\times6\times5\times4\times3\times2\times1=7!=5040$$

6. anonymous

d

7. anonymous

thank you