A bag contains six white marbles and five red marbles.

Solution:

We know that,

nCr

$=\frac{n !}{r !(n-r) !}$

According to the question,

Number of white marbles = 6,

Number of red marbles = 5

Total number of marbles = 6 white + 5 red = 11 marbles

(a)If they can be of any colour

Then, any 4 marbles out of 11 can be selected

Therefore, the required number of ways =11C4

(b) two must be white and two red

Number of ways of choosing two white and two red = 6C2 × 5C2

(c) they must all be of the same colour

Then, four white marbles out of 6 can be selected = 6C4

Or, 4 red marbles out of 5 can be selected = 5C4

 

Therefore, the required number of ways = 6C4+5C4