Three numbers are chosen from the set {1,2,...,20} . The number of ways in which this can be done so that the minimum of the chosen number is 3 or its maximum is 17 is

Number of ways of choice with 3 as minimum   = 17C2 Number of ways of choice with 17 as maximum                = 16C2 Number of ways of choice with 3 as minimum and 17 as maximum         = 13Required number of ways = 17C2+16C2−13=243