Question

If the number of arrangements of n-1 things taken from n different things is k times the number of arrangements of n-1 things taken from n things in which two things are identical then the value of k is

• A. $\frac{1}{2}$
• B. 2
• C. 4
• D. none of these

Answer 1

Answer: (B)

2

Selection of n-1 things from n things is
$={}^n{C}_{n-1}$
$=n$
$=a$
And Selection of n-1 things from n things is if two are identical
$=\frac{1}{2!}.{}^n{C}_{n-1}$
$=\frac{n}{2}$
$=b$
Therefore
$a=kb$
or
$k=\frac{a}{b}$
$=2$