The number of ways in which coins of denominations of rupees 2, 5 and 10 can be combined to make a value of rupees 50 is

Count non-negative solutions of 2a + 5b + 10c = 50: c=0 gives b even 0..10 (6 ways), c=1: 5, c=2: 4, c=3: 3, c=4: 2, c=5: 1, total 21 combinations (zero coins of a denomination allowed). If every denomination had to be used, the count would fall to only 6.