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  • 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.

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.
 

Answers (1)

Total number of marbles=6W+5R=11 

a.If they can be of any color we have to select 4 out of 11 marbles= 11C_4

b.2 white marbles can be selected in ^6C_2ways and 2 red marbles in ^5C_2.

Total number of ways= ^6C_2*^5C_2=15*10=150

c. If they all are of same color 4 white out of 6 marbles can be selected in ^6C_4ways and

4 red out of 5 can be selected in ^5C_4 ways 

   Required number of ways=^6C_4+^5C_4=15+5=20

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infoexpert21

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