Ravi is preparing gift envelopes using currency notes of the following denominations: ₹20, ₹100, ₹250, ₹400, and ₹1000. He wants each gift envelope to contain a sum made by combining at least three different denominations, and no denomination should be repeated in any envelope. How many different total amounts can Ravi prepare this way?
(a) 10
(b) 18
(c) 16
(d) 14

Question

Ravi is preparing gift envelopes using currency notes of the following denominations: ₹20, ₹100, ₹250, ₹400, and ₹1000. He wants each gift envelope to contain a sum made by combining at least three different denominations, and no denomination should be repeated in any envelope. How many different total amounts can Ravi prepare this way?
(a) 10
(b) 18
(c) 16
(d) 14

TutorArc · Accepted Answer

He has 5 distinct denominations: ₹20, ₹100, ₹250, ₹400, ₹1000.
We count how many unique combinations are possible using at least 3 denominations.
5C3 = 10
5C4 = 5
5C5 = 1
Total = 10 + 5 + 1 = 16 combinations
Each combination gives a unique sum since denominations are distinct &rarr; so 16 unique amounts.
Hence, option c is correct.

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Ravi is preparing gift envelopes using currency notes of the following denominations: ₹20, ₹100, ₹250, ₹400, and ₹1000. He wants each gift envelope to contain a sum made by combining at least three different denominations, and no denomination should be repeated in any envelope. How many different total amounts can Ravi prepare this way? (a) 10 (b) 18 (c) 16 (d) 14

Combinations and Permutations

Counting Principles

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