In a guidebook on Italy, you find 10 cities you wish to visit, but only have time on your upcoming trip to visit 4. How many unique itineraries are possible for you to choose?

Question

anonymous · Answer

$$\dbinom{10}{4}$$

anonymous · Answer

will show you how to compute this if you like.

anonymous · Answer

$$\frac{10\times 9 \times 8 \times 7}{4 \times 3 \times 2}=10\times 3 \times 7=210$$

anonymous · Answer

thank you, i had no idea how to do this

anonymous · Answer

I am assuming that when it says "itineraries" that the order you visit the cites in does not matter.  If the order does matter, then ignore the denominator and just compute $$10\times 9 \times 8 \times7$$