+119 How many numbers (up to a maximum of four digit numbers) can be made from the digits 2, 3, 4, and 5 if no digit can be repeated?
I don't think I've gone over this yet in my course's material so I really have no clue how to even start answering this problem. Any help would be appreciated, as always...
+129852 1 dgit numbers = 4
2 digit numbers = take any 2 of 4 numbers and permute them = P(4,2) = 12
3 digit numbers = take any 3 of 4 numbers and permute them = P(4,3) = 24
4 digit numbers = permute all 4 numbers = 4! = 24
So.....
4 + 12 + 2(24) = 64 numbers
1- permutations{(2,3,4,5), 1}
{2} | {3} | {4} | {5} (total: 4)
2 -permutations{(2,3,4,5), 2}
{2, 3} | {2, 4} | {2, 5} | {3, 2} | {3, 4} | {3, 5} | {4, 2} | {4, 3} | {4, 5} | {5, 2} | {5, 3} | {5, 4} (total: 12)
3-permutations{(2,3,4,5), 3}
{2, 3, 4} | {2, 3, 5} | {2, 4, 3} | {2, 4, 5} | {2, 5, 3} | {2, 5, 4} | {3, 2, 4} | {3, 2, 5} | {3, 4, 2} | {3, 4, 5} | {3, 5, 2} | {3, 5, 4} | {4, 2, 3} | {4, 2, 5} | {4, 3, 2} | {4, 3, 5} | {4, 5, 2} | {4, 5, 3} | {5, 2, 3} | {5, 2, 4} | {5, 3, 2} | {5, 3, 4} | {5, 4, 2} | {5, 4, 3} (total: 24)
4-permutations{(2,3,4,5), 4}
{2, 3, 4, 5} | {2, 3, 5, 4} | {2, 4, 3, 5} | {2, 4, 5, 3} | {2, 5, 3, 4} | {2, 5, 4, 3} | {3, 2, 4, 5} | {3, 2, 5, 4} | {3, 4, 2, 5} | {3, 4, 5, 2} | {3, 5, 2, 4} | {3, 5, 4, 2} | {4, 2, 3, 5} | {4, 2, 5, 3} | {4, 3, 2, 5} | {4, 3, 5, 2} | {4, 5, 2, 3} | {4, 5, 3, 2} | {5, 2, 3, 4} | {5, 2, 4, 3} | {5, 3, 2, 4} | {5, 3, 4, 2} | {5, 4, 2, 3} | {5, 4, 3, 2} (total: 24)
Total =4 + 12 + 24 + 24 = 64 - permutations.
