# SOLUTION: How many 6 digit numbers can be made with any combination and permutation of 3 and 7? (e.g. 377777, 737777, 777333, 733733, 333337)

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 Question 156377: How many 6 digit numbers can be made with any combination and permutation of 3 and 7? (e.g. 377777, 737777, 777333, 733733, 333337)Answer by jim_thompson5910(28595)   (Show Source): You can put this solution on YOUR website!Let's try to find the number of combinations that 3 and 7 can make up for a two digit number. Let's try a smaller example. So let's use the numbers 3 and 7 to make a two digit number, three digit number, and a four digit number to see what is going on So let's list ALL of the possible two digit numbers: 33 37 73 77 So for a two digit number, there are 4 possible combinations ----------------------------- So let's list ALL of the possible three digit numbers: 333 337 373 377 733 737 773 777 So for a three digit number, there are 8 different combinations. ----------------------------- So let's list ALL of the possible four digit numbers: 3333 3337 3373 3377 3733 3737 3773 3777 7333 7337 7373 7377 7733 7737 7773 7777 So for a four digit number, there are 16 different combinations. Notice how the number of combinations keeps doubling (since 2 doubles to 4, 4 doubles to 8, 8 doubles to 16, etc...). So if we write out a 5 digit number only using 3 and 7, then we will list out 32 different combinations (which is double of 16). And finally for a six digit number, there will be 64 different combinations (which is double of 32). Note: the quicker way (ideally once you understand what's going on) is to use this formula where is the number of digits and is the number of unique number combinations. So in this case, and . So once again, we get 64 different combinations. -------------------------------------------------- Answer: So there are 64 unique 6 digit numbers that can be generated from just the two values 3 and 7.