The number of 5-digit natural numbers, such that the product of their digits is 36 , is __________.
Answer (integer)
180
Solution
<p>Factors of 36 = 2<sup>2</sup> . 3<sup>2</sup> . 1</p>
<p>Five-digit combinations can be</p>
<p>(1, 2, 2, 3, 3) (1, 4, 3, 3, 1), (1, 9, 2, 2, 1)</p>
<p>(1, 4, 9, 11) (1, 2, 3, 6, 1) (1, 6, 6, 1, 1)</p>
<p>i.e., total numbers</p>
<p>$${{5!} \over {2!2!}} + {{5!} \over {2!2!}} + {{5!} \over {2!2!}} + {{5!} \over {3!}} + {{5!} \over {2!}} + {{5!} \over {3!2!}}$$</p>
<p>$= (30 \times 3) + 20 + 60 + 10 = 180$.</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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