BCA Semester 1 – Mathematics I – Unit 6: Permutation and Combination

$\textbf{Given:}$ Digits: $1, 2, 3, 4, 5, 6$ We are to form numbers with at least three different digits. $\textbf{Solution:}$ $\textbf{Step 1:}$ Count numbers with exactly $3$, $4$, $5$, and $6

$\textbf{Problem a:}$ A bag contains $8$ red balls and $5$ blue balls. Find the number of ways to draw $3$ red balls and $4$ blue balls.}$ $\textbf{Step 1:}$ Number of ways to select $3$ red balls fro

$\textbf{Given:}$ There are $7$ men and $3$ ladies. We need to form a committee of $6$ persons with at least one lady. $\textbf{Step 1:}$ Total ways to select $6$ persons without restriction: \[ \bi

$\textbf{Given:}$ Form three-digit numbers using digits $1,2,3,4,5,6$ with all digits different and number $<500$. $\textbf{Step 1:}$ Consider the hundreds digit. Since the number must be $<500$, hund