Question

In a library, there are $4$ science books, $4$ maths books and $3$ political science books all of which are on different topics. The number of ways in which at least one book of each subject is selected, is

• A. $1023$
• B. $2047$
• C. $961$
• D. $1575$

Answer 1

The correct option is D $1575$

The number of ways of selecting at least one book of each subject is
$({}^4{C}_1+{}^4{C}_2+{}^4{C}_3+{}^4{C}_4)\times ({}^4{C}_1+{}^4{C}_2+{}^4{C}_3+{}^4{C}_4)\times ({}^3{C}_1+{}^3{C}_2+{}^3{C}_3)=(2^4-1\left)\right(2^4-1\left)\right(2^3-1)=15\times 15\times 7=1575$