Arrangements of digits with first position restricted for JEE

Formula

\(\text{If first position has }a\text{ choices and remaining positions have }b_2,b_3,\dots,b_k\text{ choices, total}=a\,b_2b_3\cdots b_k\)

Variables: \(a,b_2,\dots,b_k\) denote available choices at positions.

Conditions: Use position-wise counting; often first digit of a number cannot be zero.

Number formation problems from digits with/without repetition.