A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles
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.
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Total number of marbles = 6 white +- 5 red = 11 marbles
(a) If they can be of any colour means we have to select 4 marbles out of 11
∴ Required number of ways = 11C4
(b) Two white marbles can be selected in 6C2
Two red marbles can be selected in 5C2 ways.
∴ Total number of ways = 6C2 x 5C2 = 15 x 10 = 150
(c) If they all must be of same colour,
Four white marbles out of 6 can be selected in 6C4 ways. And 4 red marbles out of 5 can be selected in 5C4 ways.
∴ Required number of ways = 6C4 + 5C4 = 15 + 5 = 20
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