## anonymous one year ago Find the number of 5-digit numbers that can be formed the digits 1,2,4,6,8 (when no digit is repeated) but, i)the digits 2 and 8 are next to each other ii)the numbers2 and 8 are not next to each other Best and simplest solution gets a medal

1. ganeshie8

put 2, 8 in one bag : |dw:1434301423566:dw|

2. ganeshie8

then you see just $$4$$ objects, which can be permuted in $$4!$$ ways also 2,8 inside the bag can be permuted in $$2!$$ ways for each of the above permutations so total possible 5 digit numbers using the given digits w/o repetition that contain 2,8 together would be $$4!\times 2!$$

3. anonymous

stunning @ganeshie8 what about part ii)? I also found the solution but the method was too long and complicated thanks but please answer the second part too....

4. anonymous

or is it like 5! - 48?

5. ganeshie8

that will do for part ii!

6. anonymous

thanks again....

7. ganeshie8

np:)