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Question Number 224398 by Mingma last updated on 08/Sep/25

Commented by mr W last updated on 08/Sep/25

are 10−5−8, 10−8−5, 5−10−8  different combinations?

$${are}\:\mathrm{10}−\mathrm{5}−\mathrm{8},\:\mathrm{10}−\mathrm{8}−\mathrm{5},\:\mathrm{5}−\mathrm{10}−\mathrm{8} \\ $$$${different}\:{combinations}? \\ $$

Commented by Mingma last updated on 09/Sep/25

They are just examples

Commented by mr W last updated on 09/Sep/25

i know they are examples. but are  they 3 different “combinations” or  they are the same “combination”?

$${i}\:{know}\:{they}\:{are}\:{examples}.\:{but}\:{are} \\ $$$${they}\:\mathrm{3}\:{different}\:``{combinations}''\:{or} \\ $$$${they}\:{are}\:{the}\:{same}\:``{combination}''? \\ $$

Commented by Mingma last updated on 09/Sep/25

I would love to see your solution for both same and different combinations, Prof!

Commented by mr W last updated on 09/Sep/25

to select the first number there are  40 possibilities.  to select the second number there are  35 possibilities.  40×(2×32+2×31+31×30)=42240 ✓

$${to}\:{select}\:{the}\:{first}\:{number}\:{there}\:{are} \\ $$$$\mathrm{40}\:{possibilities}. \\ $$$${to}\:{select}\:{the}\:{second}\:{number}\:{there}\:{are} \\ $$$$\mathrm{35}\:{possibilities}. \\ $$$$\mathrm{40}×\left(\mathrm{2}×\mathrm{32}+\mathrm{2}×\mathrm{31}+\mathrm{31}×\mathrm{30}\right)=\mathrm{42240}\:\checkmark \\ $$

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