How many numbers with three distinct digits have digits from {1,2,3,4,5} and a digit is 3?

1 Answer
MathFact-orials.blogspot.com
Aug 28, 2017

36

Explanation:

We have the numbers 1, 2, 3, 4, 5 to choose from to make 3 digit numbers and one of those numbers needs to be a 3. That means we can look at this problem this way - of the three digits, we can put a 3 in the first digit:

3XX

leaving four digits to put into the X places. Since this will also be true with the 3 here:

X3X

and here

XX3,

we can then say that whatever result we get for the first option we can then multiply by 3 to find all the options.

As far as choosing the remaining two numbers , we can either find that directly:

4xx3=12

or go via the permutation route (permutation because we care about order) to get to:

P_(n,k)=(n!)/((n-k)!); n="population", k="picks"

P_(4,2)=(4!)/((4-2)!)=(4!)/(2!)=(4xx3xx2!)/(2!)=4xx3

Putting it all together, we get:

(4xx3)xx3=36

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