<s>[INST] Probability of a target being hit I don't have the answer of the following question so I wanted to cross check my solution.

$A$ can hit a target 3 times in 5 shots, $B$ 2 times in 5 shots and $C$ 3 times in 4 shots. Find the probability of the target being hit at all when all of them try.

my method
P(target being hit) = $$ \frac{3}{5}*\frac{3}{5}*\frac{1}{4} + \frac{3}{5}*\frac{3}{5}*\frac{3}{4} + \frac{3}{5}*\frac{2}{5}*\frac{1}{4} + \frac{3}{5}*\frac{2}{5}*\frac{3}{4} + \frac{2}{5}*\frac{3}{5}*\frac{3}{4} + \frac{2}{5}*\frac{2}{5}*\frac{1}{4} = 0.82$$
$$ = HMM + HMH + HHM + HHH + MMH + MHM$$
where, H = hit & M  = miss
 [/INST] There is also a way we can use we take all the probable situations and subtract the ones that we don't succeed hitting;
For $A$ it is $\dfrac{2}{5}$
For $B$ it is $\dfrac{3}{5}$
And for $C$ it is $\dfrac{1}{4}$ 
$$1-\frac{2}{5}\frac{3}{5}\frac{1}{4}=\frac{47}{50}$$
I accidentally wrote this answer without seeing the first one, but I am not going to delete my effort. (Sorry:() 
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