If m denotes the number of 5 digit numbers if each successive digits are in their descending order of magnitude and n is the corresponding figure, when the digits are in their ascending order of magnitude then (m

Engineering

Mathematics

Fundamental Principal of Counting

Total Number of Combinations

Grid Problems

Question

If m denotes the number of 5 digit numbers if each successive digits are in their descending order of magnitude and n is the corresponding figure, when the digits are in their ascending order of magnitude then (m – n) has the value

⁹C₃

¹⁰C₃

¹⁰C₄

⁹C₅

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m – n = ¹⁰C₅ – ⁹C₅ = ²5₂ – 125 = 126 = ⁹C₅ or ⁹C₄
Alternatively: ⁹C₅ + ⁹C₄ – ⁹C₅ = ⁹C₄ = ⁹C₅