A class has 21 students. Eight of the students are boys and thirteen are girls.
Five students are asked to come to the board.
In how many ways can the five students be selected to come to the board, where
the order of the students does not matter, but at least two of the students are
girls?
First we calculate the number of ways any 5 of the 21 students could come
to the board regardless of their sex.
That's 21C5 = 20349 ways
From that we must calculate and subtract:
1. The number of ways 5 boys and 0 girls can come to the board.
That's 8C5 = 56 ways
2. The number of ways 4 boys and 1 girl can come to the board.
We select the girl 13 ways, and the 4 boys 8C4 = 70 ways.
Thats (13)(70) = 910 ways
Answer 20349 - 56 - 910 = 19383 ways
Edwin