A teacher must select four members of the math club to participate in an upcoming competition. How many ways are there for her to make her selection if the club has 12 members?
My answer : So we have to pick 4 people from a 12-members club. It should be : $12×11×10×9$ but apparently this is not the good answer "Incorrect She is selecting a 4-subset from the 12 kids in the club so it's $\binom{12}4$ or $\binom{12}8$"
Anyone can explain it to me?
Since order does not matter in the selection, and there are $4!$ ways to permute a selection, $12×11×10×9$ must be divided by $4!$ to arrive at the correct answer, and this is equivalent to $\binom{12}4$.