GWD 23-Q9/ Q30 呆腦算不出來

救救我啊...七月要考了

1. if S is the sum of all the integers from 1 to 30, inclusive, what is the greatest prime factor of S? Answer: 31

我算出3個吔...(1+30)*30/2=465  得出3/5/31為prime factor 啦

2. There r 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. How many possible selections of 4 books from this self include at least one paperback? answer is 50

但是我是這樣算的: 總組合為 70個: 八個中取四個(不管是paperback or hardback)

只取hardback時為六個中取四個: 15個組合

70-15=55 (為at least one is paperback ) 但為什麼答案是50個呢 !!!!