i need tp put a 7 digit number into all possible sequences?

Answer 1

A permutation is the arrangement of things when order matters. In this case order matters, because when you add digits to a number, different orders make completely different numbers. For this reason, we're doing a permutation problem.

We're arranging 7 elements (seven different digits), taken 7 at a time (since the number is a seven-digit number). Therefore...:

We need to do P(7,7), which can also be written as 7 P 7:

P(n,r) = n!/(n - r)!

P(7,7) = 7!/(7 - 7)!

= 7!/0!

= 7!

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

= 5,040

*** What this answer tells us is that, if we were given an already-made 7-digit number, there are 5,040 different ways to arrange those already-chosen digits. We can only use what we're given. For example, let's say I gave you the 7-digit number 1234567. Using JUST the digits here, the are 5,040 different ways to arrange these digits. Of all those rearrangements, 1111111 is NOT a possible number. We are only given a SINGLE 1. We just make rearrangements with what we're ALREADY GIVEN.

The guy directly above me gave an answer of 10^7. His answer is wrong, but I understand what he's saying. His answer, 10^7, is the number of ALL the POSSIBLE 7-digit numbers that can be made, using ANY digits (0-9). This doesn't apply to our problem. Read the problem again:

"i need tp put a 7 digit number into all possible sequences"

This shows that we ALREADY have a 7-digit number. We just have to rearrange those given 7 digits.

* Joe S had it right, but he should have gone into depth. He didn't even mention permutations, but just did 7! right off the bat. What he did is apply something called the Fundamental Counting Principle.

Answer 2

There are 10^7 = 10,000,000 possible sequences. You essentially have to count from 0 to 9,999,999 using leading 0's.

Answer 3

Are all digits different? Can any digit repeat? You need to know this before hand.

Answer 4

5040...if by "all possible sequences" you mean all the different ways you can arrange the numbers.

7! (factorial), means 7x6x5x4x3x2x1=5040

Answer 5

Start with the first and keep changing.
For example.
1,2,3,4,5,6,7
1,3,2,4,5,6,7
1,4,2,3,5,6,7