A car salesman talks to 10 clients during the course of a day. Each contact is recorded as either a success or a failure. For a particular day, he records 3 successes and 7 failures. Letting s denote failure, a typical arrangement of contacts is as follows: afffafafff. How many such arrangement are possible? Here we have n=10 objected; x=3 are of one type, namely, successes; the rest, n- x = 10-3 = 7, are of another type, namely failures. By the formula for counting recognizably different patterns, there are