Meiosis and combinations of chromosomes
It would be right if there were no recombination (see also crossing over) and no new mutations. However, there are crossover and there are mutations and hence the calculation is wrong.

Segregation

You have solved this problem yourself. You assumed that chromosomes segregate perfectly independently which is a rather sound assumption. The probability is $\frac{1}{2^{46}}$

Recombination

Assuming a genome-wide recombination rate of 22.8 (Wang et al. 2012) and assuming that the number of recombination is Poisson distributed, then the probability of no recombination is $e^{-22.8} ≈ 1.25\cdot 10^{-10}$.

Multiply this number by $\frac{1}{2^{46}}$ and you get about $1.8 \cdot 10^{-24}$. I would note however, that the assumption that the number of crossover is Poisson distributed might not hold (even if it is how it is typically modelled)

Mutation

Now assuming a genome-wide mutation rate of 45 (Rhabari et al. 2016), and assuming that the number of mutations is Poisson distributed, then the probability of no mutation to happen is $e^{-45} ≈ 2.9 \cdot 10^{-20}$.

Hence the probability becomes $\frac{1}{2^{46}} \cdot e^{-22.8} \cdot e^{-45} ≈ 10^{-44}$.

Note that we assumed that the number of mutations and the number of crossovers are independent which is definitely wrong. If we were to know the correlation, we could make better estimates. This would bring our estimate to some higher probability.