How many ways can a four digit number be formed with different restrictions?

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SUMMARY

This discussion focuses on the calculation of permutations and combinations, specifically in the context of arranging letters and distributing items. Key examples include the arrangement of the letters in "MISSISSAUGA" and "BASKETBALL," with calculations using factorials and the formula n!/(p!q!r!). The discussion also addresses how to form four-digit numbers under various restrictions, such as using digits 1 to 8 or 0 to 7, and the requirement for numbers to be odd or even. The participants clarify the correct application of permutations and combinations, emphasizing the importance of understanding these concepts for accurate problem-solving.

PREREQUISITES
  • Understanding of permutations and combinations
  • Familiarity with factorial notation (n!)
  • Basic knowledge of number theory (odd and even numbers)
  • Ability to apply the formula n!/(p!q!r!) for arrangements
NEXT STEPS
  • Study the concept of permutations in detail, focusing on the formula n!/(p!q!r!).
  • Learn how to calculate combinations and their applications in real-world scenarios.
  • Explore the principles of counting and restrictions in combinatorial problems.
  • Practice solving problems involving arrangements of letters and distributions of items.
USEFUL FOR

Students, educators, and anyone interested in combinatorial mathematics, particularly those studying permutations and combinations for academic purposes or competitive exams.

  • #31
Erzeon said:
From the question you wrote, you can't repeat the same number,
ok, i get it...

but this one i don't get it...the last number should be odd because when it's odd, it produces an odd number
 
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  • #32
i mean last digit, odd numbers always have their last digit as an odd number.
 
  • #33
ohh, i know what you mean now... so the answer in 4d would be...still figuring out...lol
 
  • #34
is it 9!/5! or 9x8x7x6 for 4d? since the numbers runs from 0 to 9, but there is only 5 odd numbers, and same thing with 4e?
 

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