Question

The number of ways of selecting $8$ books from a library which has $9$ identical books each on Mathematics. Physics, Chemistry and English is

• A. $165$
• B. $166$
• C. $167$
• D. $168$

Answer 1

The correct option is A $165$

$\text{No of Maths books}=x_1$

$\text{No of Physics books}=x_2$

$\text{No of Chemistry books}=x_3$

$\text{No of English books}=x_4$

$x_1+x_2+x_3+x_4=8$

All are identical so Total no. of ways can be calculated by formula

$n+r-1_{C_{r-1}}$

$8+4-1_{C_{4-1}}$ $={11}_{C_3}$

$=165$