Question:
Find the values of
(i) ${ }^{200} \mathrm{C}_{198}$,
(ii) ${ }^{76} \mathrm{C}_{0}$,
(iii) ${ }^{15} \mathrm{C}_{15}$
Solution:
(i) ${ }^{200} C_{198}$ $=\frac{200 !}{198 !(200-198) !}=\frac{200 !}{198 ! 2 !}=\frac{200 \times 199}{2 !}=100 \times 199=19900$
(ii) ${ }^{76} \mathrm{C}_{0}$ $=\frac{76 !}{0 ! 76 !}=1_{[\text {As } 0 !=1]}$
(iii) ${ }^{15} \mathrm{C}_{15}$ $=\frac{15 !}{15 ! 0 !}=1$