JEE Main 2020 (Online) 8th January Morning ShiftQuestion 1
An urn contains $5$ red marbles, $4$ black marbles and $3$ white marbles. Then the number of ways in which $4$ marbles can be drawn so that at the most three of them are red is ________.
Permutation and Combination
Answer$490$
Solution
Concept. "At most three red" fails only when all $4$ are red. Formulas used. (1) ${}^{12}C_4=495$, ${}^5C_4=5$Step 1 - All selections. $5+4+3=12$ marbles: ${}^{12}C_4=495$. Step 2 - All four red. ${}^5C_4=5$. Step 3 - Subtract. $495-5=490$. Answer: 490