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.
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