Answer:
See explanation
Step-by-step explanation:
Total number of letters = n! = 10
Permutation for 10 letters = n!
= 10!
= 10*9*8*7*6*5*4*3*2*1
= 3628800
From n letters:
Number of A = 2
Number of C = 2
Number of L = 2
A₁, A₂, C₁, C₂, L₁, L₂, O, R, T, U
Out of 3628800 permutations the word calculator can be spelled as:
C₁ A₁ L₁ C₂ U L₂ A₂ T O R
C₂ A₂ L₂ C₁ U L₁ A₁ T O R
and so on
So total number of different permutations are
(permutation of number of letters) / permutation of (number of As * number of Cs * number of Ls)
= 10! / (2! 2! 2 !)
= 10*9*8*7*6*5*4*3*2*1 / (2*1) (2*1) (2*1)
= 3628800 / 2 * 2 * 2
= 3628800 / 8
= 453600
Hence probability that a randomly selected permutation of the letters A, A, C, C, L, L, O, R, T, U would spell "calculator" is:
1 / total number of different permutations
= 1 / 10! / (2! 2! 2 !)
= 1/453600
= 0.000002
