Permutations

We have,

20!%20%2B%5Cfrac%7B21!%7D%7B1!%7D%20%2B%20%5Cfrac%7B22!%7D%7B2!%7D%20%2B%20...%20%2B%5Cfrac%7B60!%7D%7B40!%7D

%3D20!%20%5Cleft%5B%201%2B%5Cfrac%7B21!%7D%7B20!1!%7D%20%2B%20%5Cfrac%7B22!%7D%7B20!2!%7D%20%2B...%20%2B%5Cfrac%7B60!%7D%7B40!20!%7D%5Cright%5D

%3D%2020!%20%5Cleft%5B%5C%2C%5E%7B21%7DC_%7B0%7D%20%2B%5C%2C%5E%7B21%7DC_%7B1%7D%20%2B%5C%2C%5E%7B22%7DC_%7B2%7D%20%2B...%2B%20%5C%2C%5E%7B60%7DC_%7B40%7D%5Cright%5D

%3D%2020!%5Cleft%5B%5C%2C%5E%7B22%7DC_%7B1%7D%20%2B%20%5C%2C%5E%7B22%7DC_%7B2%7D%2B...%2B%5C%2C%5E%7B60%7DC_%7B40%7D%5Cright%5D

%5Cleft%5B%5C%2C%5E%7Bn%7DC_%7Br-1%7D%20%2B%5C%2C%5E%7Bn%7DC_%7Br%7D%20%3D%20%5C%2C%5E%7Bn%2B1%7DC_%7Br%7D%5Cright%5D

%3D%2020!%20%5Cleft%5B%20%5C%2C%5E%7B61%7DC_%7B40%7D%5Cright%5D%20%3D%2020!%20%5Ccdot%20%5C%2C%5E%7B61%7DC_%7B21%7D

Chapter Questions
1 MCQs