A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
8
12
15
21
27
(1)在水果里选一种C1 2,就有两种选择;在奶酪里选一种C1 6,就有六种选择,一共就是2*6=12种
(2)在水果里选两种C2 2,就有一种选择;在奶酪里选两种C2 6=6!/(2!*4!)=15,就有15中选择,一共就是1*15=15种
然后将上面两种情况相加,就是27中选择。
In case we serve 2 of each 6C2*2C2=15*1=15
=> 15+12=27