In how many ways a team of 11 must be selected from 5 men and 11 women such that the team comprises of not more than three men ?
How does one prove that there exist integers a , b , and c so not all are zero and each has an absolute value of less than one million , such that | a + b -LRB- 2 ^ 0.5 -RRB- + c -LRB- 3 ^ 0.5 -RRB- | < 10 ^ -11 ?