Choosing and arranging in two steps for JEE

Formula

\(\text{Number of ordered arrangements of }r\text{ chosen from }n = {}^nC_r\cdot r! = {}^nP_r\)

Variables: \(n\) is total number of distinct objects, \(r\) is number used.

Conditions: \(0\le r\le n\).

Problems naturally split into selection then arrangement.