Which equation has no solution?
1 answer:
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Solution :
The function : be a random permutation.
f is a permutation on , i.e. f is permutation 10.
Now we know that the total number of distinct permutation on to symbolize 10!.
Each of these 10! permutation to a permutation function
Therefore, total number of permutation functions are 10!.
Now we want the total number of permutation functioning :
such that f(0) = 0 and f(1)= 1
Now we notice that when f(0)=0 and f(1)=1, then two symbol '0' and '1 are fixed under permutation f.
So essentially when f(0) = 0 and f(1) = 1, f becomes permutation on 8 symbol.
Total number of permutation functioning , f(0)=0 and f(1)=1 are 8!
Now we want the probability that a random permutation satisfies f(0) = 0 and f(1) = 1.
The number of permutation function , i.e.
The probability that a random permutation satisfies f(0) = 0 and f(1) = 1 is
Therefore, the probability that a random permutation satisfies f(0)= 0 and f(1)=1 is