How many seven-digit numbers can be formed with the digits {1, 2, 4, 7} if(a) repetition ok (b) no repetition?

I just need to know the formula on how to do this, not the actual answer.How many seven-digit numbers can be formed with the digits {1, 2, 4, 7} if(a) repetition ok (b) no repetition?
a) 16384


4 to the 7th power





b) none


Only four digits can't make a seven digit number without repeating.How many seven-digit numbers can be formed with the digits {1, 2, 4, 7} if(a) repetition ok (b) no repetition?
Did you mean to list all the numbers up to 7? You can't list a seven digit number using four different digits without repeating. I'll assume you meant {1,2,3,4,5,6,7}.





Repeats OK = (number or choices)^number of selections





7 choices, 7 selected = 7^7





Repeating not OK


7 is the number of choices for your first digit, but then you only have 6 choices for your second (since you can't repeat), and 5 for your third (now you have two numbers removed), 4 choices, and so on...


7 x 6 x 5 x 4 x 3 x 2 x 1 = 7!


This calculation is common enough that you'll find it listed on a caculator with a button like x.
for first one-%26gt; 4*4*4*4*4*4*4=4^7


and for second -%26gt; 4*3*2*1*0*0*0=0