# Flags

How many different flags can be made from colors white, red, green, purple, orange, yellow, blue so that each flag consisted of three different colors?

Result

n =  210

#### Solution:

Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Dr Math
nice site helped me very much

Math student
This solution is for if the order of color matters. However, according to the question, order does not matter. It is therefore a combination, not a permutation. The solution should be (7x6x5)/3! = 35.

Dan
I think solution in OK, because order matters...

## Next similar examples:

1. Lock
Combination lock will open when the right choice of 5 numbers (from 1 to 12 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately?
2. Cars plates
How many different licence plates can country have, given that they use 3 letters followed by 3 digits?
3. Pins 2
how many different possible 4 digits pins can be found on the 10-digit keypad?
4. Olympics metals
In how many ways can be win six athletes medal positions in the Olympics? Metal color matters.
5. Election 4
In a certain election there are 3 candidates for president 5 for secretory and 2 for tresurer. Find how many ways the election may (turn out/held).
6. Metals
In the Hockey World Cup play eight teams, determine how many ways can they win gold, silver and bronze medals.
Kamila wants to change the password daliborZ by a) two consonants exchanged between themselves, b) changes one little vowel to such same great vowel c) makes this two changes. How many opportunities have a choice?
8. Peak
Uphill leads 2 paths and 1 lift. a) How many options back and forth are there? b) How many options to get there and back by not same path are there? c) How many options back and forth are there that we go at least once a lift?
9. Medals
In how many ways can be divided gold, silver and bronze medal among 21 contestant?
10. Neighborhood
I have 7 cups: 1 2 3 4 5 6 7. How many opportunities of standings cups are there if 1 and 2 are always neighborhood?
11. Coin and die
Flip a coin and then roll a six-sided die. How many possible combinations are there?
12. 7 heroes
9 heroes galloping on 9 horses behind. How many ways can sort them behind?
13. Football league
In the 5th football league is 10 teams. How many ways can be filled first, second and third place?
14. PIN - codes
How many five-digit PIN - code can we create using the even numbers?
15. Theorem prove
We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?