Maths-
General
Easy

Question

Consider the following statements:
1. The number of ways of arranging m different things taken all at a time in which p less or equal than m particular things are never together is m! – (m – p + 1)! p!.
2. A pack of 52 cards can be divided equally among four players in order in fraction numerator 52 factorial over denominator left parenthesis 13 factorial right parenthesis to the power of 4 end exponent end fractionways.
Which of these is/are correct?

  1. Only (1)    
  2. Only (2)    
  3. Both of these    
  4. None of these    

The correct answer is: Both of these


    (1) Total number of ways of arranging m things = m!.
    To find the number of ways in which p particular things are together, we consider p particular things as a group.
     Number of ways in which p particular things are together = (m – p + 1)! p!
    So, number of ways in which p particular things are not together
    = m! – (m – p + 1)! p!
    Total number of ways = fraction numerator 52 factorial over denominator left parenthesis 13 factorial right parenthesis to the power of 4 end exponent end fraction
    Hence, both of statements are correct.

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