   SEARCH HOME Math Central Quandaries & Queries  Question from Larisa, a parent: Please tell me the answer or how to get the answer of every possible digit combination of 5173, for instance1735, 1753, 1573, 1537, 1357, 1375, etc. Hi Larisa.

Choose one of the four as the first digit. You have four choices.

Then choose one of the remaining three as the second digit. You have three choices.

Then choose either of the remaining two as the third digit and write the only remaining digit after it. There are two choices.

With permutations like this, we multiply the choices together: 4 x 3 x 2 = 24 possibilities.

Cheers,
Stephen La Rocque.

Larisa wrote back

Question from Larisa, a parent:

I recently asked how to figure out all possible combinations of 5173 but your reply was that there are 24 combinations. I want to know what those combinations are, please.

Larisa,

Actually you asked for the combinations or how to get the combinations. Steve's response does tell you how to find the combinations. He says to choose one of the 4 digits as the first digit so you have 4 possibilities. Suppose you choose 1 as the first digit. Next he says choose one of the remaining three as the second digit. Here there are 3 possibilities to extend the number from 1 digit to 2 digits. they are

13
15
17

Finally he says choose either of the remaining two as the third digit and write the only remaining digit after it. In each case there are 2 choices for the third digit and hence each of the three two digit numbers above expands to two three digit numbers. Hence this gives you six three digit numbers. In each case there is only one choice for the final digit. Thus you get

1357
1375
1537
1573 and so on.

Now go back and choose a different first digit and repeat the process.

Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.