How many ways to select atleast one book of each subject? Suppose there are $6$ books on Maths, $3$ books on English and $2$ books on science . How many ways to select atleast one book of each subject, assuming the books of same subject are different ?

My try:
I have not solved it, but I just need to check my logic.
Number of ways:-
Total ways to select $3$ books - (Total ways to select $3$ books on Maths + Total ways to select $3$ books on English + Total ways to select $3$ books on Science + Total ways to select $3$ books on Maths and English + Total ways to select $3$ books on Maths and science + Total ways to select $3$ books on Science and English)
Is this logic right ?

Select one or more Maths books. Number of ways:$\dbinom{6}{1}+\cdots+\dbinom{6}{6}=2^6-1$ 
  
Select one or more English books. Number of ways:$\dbinom{3}{1}+\cdots+\dbinom{3}{3}=2^3-1$ 
  Select one or more Science books. Number of ways:$\dbinom{2}{1}+\cdots\dbinom{2}{6}=2^2-1$ 
  
So, required ways 
$(2^6-1)(2^3-1)(2^2-1)$
