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 ___________.

Step-by-step solution

We have, 5 red, 4 black, 3 white marbles Required number of ways = C 0 5 × C 4 7 + C 1 5 × C 3 7 + C 2 5 × C 2 7 + C 3 5 × C 1 7       ​ = 35 + 175 + 210 + 70 = 490