In a flower shop there's: 20 kinds of white flowers, 15 kinds of yellow flowers, 10 kinds of purple flowers, and 10 kinds of orange flowers. How many possible ways are there to choose 7 different kinds of flowers so you end up with at least one flower for each color.
First I picked one of each flower color, which is 4 kinds of flowers total. And now the problem is to choose 3 kinds of flowers from $15+10+10+20=55$ minus $4$ $(51)$ without any conditions so the number of options to choose a subsequence of $3$ out of $51$ is $51\choose 3 $.
Is this correct? Does anybody else have a possible way of solving this problem. Thanks in advance.