Question

in how many ways could the digits in the number 458 978 be arranged if the prime digits must remain in the original position

i understand that after removing the prime digits you'd be left with 4_8 9_8 and that you have 5 spots where you can put 5 then 4 spots when you can put 7 but after that I am not sure

Answer 1

there are 4!/2! permutations of 4 things with 2 duplicates

Answer 2

thats what I had gotten but on my textbook, it says the answer is 24

Answer 3

well, they can in fact be arranged in 24 ways, but unless you can distinguish the two 8's (say, by color), only 12 will be unique.

Even textbooks can have mistakes.