Engineering Maths - Combinatories

22. Number n of license plates that can be made where each plate contains two distinct letters followed

  • Option : B
  • Explanation : n = 26 x 25 x 10 x 9 x 8=468000. i.e. there are twenty-six choices for the first letter, but only twenty-five choices for the second letter which must be different from the first letter. Similarly, choices for the digits are 10, 9 and 8 since the digits must be distinct.
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23. Suppose a licence plate contains two letters followed by three digits with the first digit not zero. How many different licence plates can be pinted?

  • Option : C
  • Explanation : Each letter can be printed in twenty-six different ways, the first digit in nine ways and each of the other two digits in ten ways. Hence 26 x 26 x 9 x 10 x 10 = 608400 different plates can be printed.
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Common data  for next 2 questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Given : npr = 3024.

24. Value of n will be

  • Option : D
  • Explanation : Since np is product of consecutive positive integers, npr=3024=9x8x7x6 Hence n=9 and r = 4
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25. Value of r will be

  • Option : B
  • Explanation : Since np is product of consecutive positive integers, npr=3024=9x8x7x6 Hence n=9 and r = 4
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