<a href="https://musing.io/q/vedvati/p3enxvznx">View this answer on Musing.io</a><br /><p><strong>TLDR - 5040 numbers can be formed using every digit (0-9) only once.</strong></p>
<p>I had a very interesting discussion with @awesomianist regarding this question. It feels good to revise our high school Maths.*</p>
<p>This question can be easily answered if we understand Permutation and Combination. &nbsp;Permutation is just an ordered Combination. In Permutation, the order matters, whereas in Combination, the order does't matter.&nbsp;</p>
<p>So there are 2 types of Permutation. One is where repetition is allowed, and another one is where repetition is not allowed.</p>
<p>To answer this question, we will have to use Permutation since the<em> order matters </em>(1234 and 4321 is 2 different numbers) and <em>repetition is not allowed</em> (1123 uses 1 twice).</p>
<p>The formula for this would be: &nbsp;<em><strong>n!/(n − r)! &nbsp;</strong></em></p>
<p><strong>But my way of understanding permutation is this:</strong></p>
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<p><img src="https://images.unsplash.com/photo-1500031722107-c33111e78dd0?ixlib=rb-0.3.5&s=5d304ea147ab7c8bd2252db2fe49cb97&auto=format&fit=crop&w=1050&q=80" /></p>
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<p>I imagine 4 empty chairs representing the 4 digit numbers. &nbsp;Now I name them seat A, B, C and D.</p>
<p>_ &nbsp;_ &nbsp;_ &nbsp;_</p>
<p>And there are 10 people, each representing the digit 0 - 9.</p>
<p>10 people can choose to sit on seat A, but once a person sit on seat &nbsp;A, the next 9 people can choose to sit on seat B. Now there's 8 people left and they can choose to sit on seat C and the 7 people that are left can now choose to sit on seat D.</p>
<p>Now we only need to multiply 10 by 9 by 8 by 7 (10*9*8*7), which equals to 5040.</p>
<p><strong>So there are 5040 numbers can be formed using every digit only once in the number.</strong></p>
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