Question

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 $\frac{52!}{(13!)^{4}}$ ways.

Which of these is/are correct?

• A. Only (1)
• B. Only (2)
• C. Both of these
• D. None

Answer 1

Answer: (C)

Both of these

Answer 2

(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 = $\frac{52!}{(13!)^{4}}$

Hence, both of statements are correct.