In how many ways can the letters of the word 'ALGEBRA' be arranged, so that two A's are never together?

In how many ways can the letters of the word ARRANGE be arranged so that two R's are never together ?

In how many ways can the letters of the word ARRANGE' be arranged

In how many ways can the letters of he word ARRANGE be arranged so that the two A's are together but not two R's

In how many ways, the letters of the word 'ARMOUR' can be arranged?

In how many ways, the letters of the word 'BANKING' can be arranged?

In how many ways can the letters of the word PLANTAIN be arranged so that the two A do not come together?