how many ways can you arrange numbers 12345678in groups of 4's? Please show work?

Question

examples 1234
5678
2436

Answer 1

Assuming order matters, then it is
P(8,4) = 8*7*6*5 = 1680

Answer 2

This is a questiopn from permutations and combinations.

First Choose 4 nos from the given eight numbers. This can be done in 8C4 ways.

Now Arrange those 4 in all the four places in the four digited number. This can be done in 4p4 ways

Since both the jobs are connected with and we should multiply both these numbers. Therefore the answer is 8c4*4p4
= (8*7*6*5)/(4*3*2*1)*4!
= 70*24
= 1680

Hope you are clear with this explaination.

Answer 3

First Choose 4 nos from these 8
= 8C4
and
arrange those 4 in all the orders
=4p4
Therefore 8c4*4p4
= (8*7*6*5)/(4*3*2*1)*4!
=70*24
=1680

Answer 4

Since your answer says "groups of 4's" I'm assuming that you mean two groups.

If the you are partitioning the 8 digits into two groups of 4, then there will be 8!/4!4! = 70 different partitioning.

If the ordering matters, then 8! = 40320 ways.
There are 8! ways to order the 8 digits. For each ordering , divide it in the middle to get two ordered groups of 4.

Answer 5

well for the first number you can select 8 different options, for the 2nd you have 7 options assuming you can only use each number once. For the 3rd you have 6 options and for the 4th you have 5 options so its.

8*7*6*5=1680 different combinations.

Answer 6

we will select the no.s one by one
first number can be selected in 8 ways ( because there are 8 no.s)
second no. can be selected in 7 ways ( there are only 7 no.s left)
third in 6 ways and fourth in 5 ways
so total no. of ways of selecting = 8*7*6*5
=1680

Answer 7

nPr = (n!)/((n - r)!)
8P4 = (8!)/((8 - 4)!)
8P4 = (8!)/(4!)
8P4 = 1680 different ways