Question

A shelf has 4 books, of which 2 are of science and 2 are of social studies. In how many ways can we select 3 books from the shelf such that we have atleast one science book and atleast one social studies book?

Answer 1

Solution:

Total = 4 books

2 are of science

2 are of social studies

Required number of ways = (1 science, 2 social studies)+(2 science, 1 social studies)

$=\ ^2C_1\ ^2C_2+\ \ ^2C_2\ ^2C_1 \\ =2\times 1+1\times 2 \\ =2+2 \\=4$