Form 4 digit numbers using $\{1,2,3,4,5\}$
a) In some of the numbers, digits are distinct.
b) The number is even.
Solve for just $a$, just $b$, and for both $a$ and $b$.
I could not understand what is meant in part $a$. Is not it same with the set of all $4$ digit numbers written with $\{1,2,3,4,5\} = 5 \cdot 5 \cdot 5 \cdot 5$?
$\endgroup$ 22 Answers
$\begingroup$$(a)$ asks you to find $4$-digit numbers with digits in $\{1,2,3,4,5\}$ for which the digits are distinct, i.e. 1234 or 3245, and $(b)$ wants you to find even $4$-digit numbers with digits in $\{1,2,3,4,5\}$, i.e. 2344 or 5432. Then it wants you to find even 4-digit numbers with distinct digits, i.e. 5412.
$\endgroup$ 6 $\begingroup$Solution for (just a): 5432 = 5! = 120 Solution for (just b): 5552 = 250 (Numbers may not be distinct) Solution for (both a and b): 432*2 = 48 (Numbers are distinct digit and even)
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