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 ?

I think its not work. As you are not including one subject in all 3 cases.
I think more easy way is to find -

Total cases - (Cases with only 1 subject books selected + 2 subjects books selected)

