共 and 由……组成: in total, made up of
【四06】【四31】副词、固定格式 / adverbs
Tone colorsā tone 1á tone 2ǎ tone 3à tone 4a neutral
共 is the written, slightly formal form of 一共 ("in total"). It goes after the subject and before the verb or the number: 我们班共有三十个学生, 这本书共十五课. It can also mean "jointly" (共同, 共享).
由……组成 says what a whole is made of: the whole is the subject and the parts come after 由: 我们班由两位老师和二十位学生组成. It often sits inside a 是……的: 这个小组是由五个人组成的.
一共 suits any conversation (一共多少钱？); 共 is more for reports, announcements and texts. Don't confuse 由……组成 with 包括 ("to include"): 包括 may name only some of the parts, 由……组成 gives all of them.
Examples
我们班共有三十个学生。
Wǒmen bān gòng yǒu sānshí ge xuésheng.There are thirty students in our class in total.
这本书共十五课。
Zhè běn shū gòng shíwǔ kè.This book has fifteen lessons in all.
这次旅行，我们共花了五千块。
Zhè cì lǚxíng, wǒmen gòng huā le wǔ qiān kuài.On this trip we spent five thousand yuan in total.
我们的小组由两个中国人和三个外国人组成。
Wǒmen de xiǎozǔ yóu liǎng ge Zhōngguórén hé sān ge wàiguórén zǔchéng.Our group is made up of two Chinese and three foreigners.
这个家由爷爷奶奶、爸爸妈妈和两个孩子组成。
Zhè ge jiā yóu yéye nǎinai, bàba māma hé liǎng ge háizi zǔchéng.This family consists of the grandparents, the parents and two children.
这次考试由听力、阅读和写作三个部分组成。
Zhè cì kǎoshì yóu tīnglì, yuèdú hé xiězuò sān ge bùfen zǔchéng.This exam has three parts: listening, reading and writing.
Common mistakes
✗ 共我们三个人 → ✓ 我们共三个人 (共 comes after the subject).
✗ 这个班组成两位老师和二十位学生 → ✓ 这个班由两位老师和二十位学生组成 (the whole is the subject, the parts are introduced by 由).