Incorrect problem?

None problem's answers don't seem correct.

If five digits are selected from a set containing {6, 5, 4, 3, 2, 1}, then the largest password is 66666 and the smallest is 00000. Therefore, the sum of all the possible passwords would be $\sum _{ n=1 }^{ 66666 }{ n=\frac { 66666(66667) }{ 2 } =2222211111 }$ .

What do you guys think?

#Combinatorics

Easy Math Editor

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Comments

You're incorrect.

Try listing down the first few smallest 5-digits that satisfy this condition and you will notice that not all 5-digit integers satisfy this condition.

Pi Han Goh - 5 years, 4 months ago

Oh, you're right, it completely flew over my head! The second I read your reply and counted, "Well, 1, 2, 3, 4, 5, 6, 7... Wait a second...". Thank you for clearing this all up for me! :)

Andrew Tawfeek - 5 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$