Q. How many four digit numbers can be formed using the digits 1, 2, 3, 4, 5 such that at least one of the digit is repeated?
A) $4^{4} - 5!$
B) $4^{5} - 4!$
C) $5^{4} - 4!$
D) $5^{4} - 5!$
Explanation
(d)
When repetition is allowed then, number of four digits numbers that can be formed using 1, 2, 3, 4, 5$= 5^{4}$
and when repetition of digits is not allowed, then number of 4 digits numbers which can be formed is $\ ^{5}P_{4} = 5!$
$\therefore$ The number of ways in which at least one digit is repeated$= 5^{4} - 5!$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.