Abdul Hakim is the Chairman of a committee. In how many ways can a committee of 5 be chosen from 10 people given that Abdul Hakim must be one of them?

If $\displaystyle ^{n}C_{3}= ^{n}C_{5'}$ then find the value of n:

$\dfrac { { C }_{ 1 } }{ { C }_{ 0 } } +\dfrac { 2{ C }_{ 2 } }{ { C }_{ 1 } } +\dfrac { { 3C }_{ 3 } }{ { C }_{ 2 } } +.....+\dfrac { { nC }_{ n } }{ { C }_{ n-1 } } =$

${ }^{n} P_{r}=54$ এবং ${ }^{n} C_{r}=9$ হলে, $r$ এর মান নির্ণয় কর।

If $(1+x)^{15}=C_{0}+C_{1}xC_{2}x^{2}+...+C_{15}x^{15},$ then $^{15}C_{0}^{2}- ^{15}C_{1}^{2}+^{15}C_{2}^{2}- ^{15}C_{2}^{3}+... ^{15}C_{15}^{2}$ is equal to