Question

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

Answer 1

put 2, 8 in one bag :

Answer 2

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 \(4!\times 2!\)

Answer 3

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....

Answer 4

or is it like 5! - 48?

Answer 5

that will do for part ii!

Answer 6

thanks again....

Answer 7

np:)