a number of, the number of 的区别
a number of:指的是"许多",谓语动词用复数
the number of:指的是"什么什么的数量",谓语动词用单数
楼主的题目中谓语动词用了第三人称单数shows。所以用the number of
例子:
A number of soldiers were detached to guard the building.
许多士兵被派去保护这座建筑物。
The number of tigers has reduced abruptly in the last fifty years.
在过去的五十年里,老虎的数目锐减。