A bag contains six white marbles and five red marbles.

Question:

A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if

(a) they can be of any colour

(b) two must be white and two red and

(c) they must all be of the same colour.

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 = 6C× 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

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