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...

Aleguan Feb 15, 2018

#1**+2 **

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

CPhill Feb 15, 2018

#2**+1 **

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.**

Guest Feb 15, 2018