문제 : A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?

정답 해설 보니까 9/10 x 8/9 x 1/8 = 1/10

1/10 + 1/10 = 1/5

라고 되어있는데

맨처음 9/10은 이해가 갔는데 secretary가 되고 treasurer이 안될확률 + secretary가 안되고 treasurer이 될 확률을

더하는 거니까 9/10 x 1/9 x 7/8 + 9/10 x 8/9 x 1/8 으로 하면 왜 안되고

왜 정답처럼 계산을 해야하는지 혹시 아시는 분 계신가요?