QJEEM20Ma5fdf: JEE Main 2020 Mathematics - Class 11 JEEM20Ma5fdf Solution: An urn contains 5 red marbles, 4 black marbles and 3 white…

Here 5 red marbels and 7 non red marbels presents.

No of ways 4 marbels can be chosen where atmost 3 red marbels can be present.

Case 1: When 3 red marbels present

No of ways = ⁵C₃ $\times$ ⁷C₁

Case 2: When 2 red marbels present

No of ways = ⁵C₂ $\times$ ⁷C₂

Case 3: When 1 red marbels present

No of ways = ⁵C₁ $\times$ ⁷C₃

Case 4: When 0 red marbels present

No of ways = ⁵C₀ $\times$ ⁷C₄

$\therefore$ Total number of ways

= ⁵C₃ $\times$ ⁷C₁ + ⁵C₂ $\times$ ⁷C₂ + ⁵C₁ $\times$ ⁷C₃ + ⁵C₀ $\times$ ⁷C₄

= 70 + 210 + 175 + 35

= 490