Consider the following statements:
1. The number of ways of arranging m different things taken all at a time in which p ≤ 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 
ways.
Which of these is/are correct?
Text Solution
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(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!
(2) Each player shall receive 13 cards.
∴ Total number of ways = 
Hence, both of statements are correct.
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