A big contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag. If (i) they can be of any colour. (ii) two must be white and two red. (iii) they must all be of the same colour.

Explanation

Total number of marbles = 6 white + 5 red = 11 marbles
(i) If they can be of any colour means we have to select 4 marbles out of 11.
`therefore` Required number of ways `=""^(11)C_(4)`
(ii) If two must be white, then selection will be `""^(6)C_(2)` and two must be red, then selection will be `""^(5)C_(2)`.
`therefore` Required number of ways `= ""^(6)C_(2) xx ""^(5)C_(2)`
(iii) If they all must be of same colour, then selection of 4 white marbles out of `6 = ""^(6)C_(4)` and selection of 4 red marble out of `5 = ""^(5)C_(4)`
`therefore` Required number of ways `=""^(6)C_(4) + ""^(5)C_(4)`