Suppose you have sufficient amount of rupee currency in three denominations : Rs. 1, Rs. 10 and Rs. 50. In how many different ways can you pay a bill of Rs. 107 ?

Answer is (c).

Case I: We use TWO Rs. 50 notes – One possibility – 50(×2) + 1(×7) = 107

Case II: We use ONE Rs. 50 note –

Six possibilities (by adding Rs.10 note from none to five) –

50(×1) + 10(×0) + 1(×47) = 107; 50(×1) + 10(×1) + 1(×47) = 107; 50(×1) + 10(×2) + 1(×37) =

107; 50(×1) + 10(×3) + 1(×27) = 107; 50(×1) + 10(×4) + 1(×17) = 107; 50(×1) + 10(×5) + 1(×7) = 107;

Case III: We use no Rs. 50 note (Only Rs. 10 and 1 notes) – Ten possibilities –

10(×10) + 1(×7) = 107; 10(×9) + 1(×17) = 107; 10(×8) + 1(×27) = 107; 10(×7) + 1(×37) = 107; 10(×6) + 1(×47) = 107; 10(×5) + 1(×57) = 107; 10(×4) + 1(×67) = 107; 10(×3) + 1(×77) = 107; 10(×2) + 1(×87) = 107; 10(×1) + 1(×97) = 107;

Case IV: We use only Rs. 1 note – One possibility – 1 (×107) = 107.

Hence, total 18 possibilities.