Q. Consider the following statement: 1.The number of ways of arranging $m$ different things taken all at a time in which $p \leq m$ perticular 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 of these
Explanation
(c)
(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 thing as a group.
$\therefore$ 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 statements are correct
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.