Question

the number of permutations of 123456 that have exactly one number in the correct place is 'n' then n equals to​

Answer 1

n = 264 the number of permutations of 123456 that have exactly one number in the correct place is 'n

Step-by-step explanation:

123456  has 6 numbers and all are different .

Hence one number out of  the six numbers which is at its correct place cam be selected  in ⁶P₁ = 6  ways

Now the remaining five are to be arranged such that none of them are at there original place  for that

5!  (1/2! -1/3! +1/4!-1/5!)

= 120 ( 1/2  -  1/6  + 1/24  - 1/120)

= 60 - 20 + 5 - 1

= 65 - 21

= 44

Total number of Ways  = 6 * 44  = 264 ways

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