A bag contains 6 white and 4 black balls. A die is rolled once and...

Given,

Bag have $6$ white and $4$ black balls

Now also given die is rolled and the number denotes the number of ball drawn from the bag,

So, probability all drawn balls are white will be,

$= \dfrac{1}{6}\left[\dfrac{C1 6}{C1 10} + \dfrac{C2 6}{C2 10} + \dfrac{C3 6}{C3 10} + \dfrac{C4 6}{C4 10} + \dfrac{C5 6}{C5 10} + \dfrac{C6 6}{C6 10}\right]$

$= \dfrac{1}{6}\left[\dfrac{6}{10} + \dfrac{15}{45} + \dfrac{20}{120} + \dfrac{15}{210} + \dfrac{6}{252} + \dfrac{1}{210}\right]$

$= \dfrac{504}{2520} = \dfrac{1}{5}$