1. A large jar contains 50 blue marbles and 50 red marbles. How many marbles mus

Question

1.  A large jar contains 50 blue marbles and 50 red marbles. How many marbles must be drawn randomly to ensure that you have three marbles of the same color

2. A ?ve person committee is to be selected from a club having 45 members. How many committees are possible ?

3. In the card game Bridge, a hand consists of 13 cards. The distribution of the hand into the various suits is important. How many Bridge hands have a suit distribution of 5-4-3-1 (i.e., ?ve cards in one suit, four in another suit, three in a third suit and one card in the fourth suit) ?

Explanation / Answer

1). Consider the case of 5 red marbles and 5 blue marbles, follow the given process to obtain 3 marbles of each colour.

divide group of 10 into 5 and 5 marbles each, One possible group is (R,R,B,B,R) and other possible is (B,B,R,B,R). Each of them have 3-3 balls of the one type.

now this same thing can be extended for 100 marbles,

Divide 100 marbles in group of 25, 25, 25 and 25.

on removing these first three group we can be still sure that atleast three marbles are there of same colour.

2). out of 45 members , 5 can be selected in 45C5 number of ways = 1221759. These many number of committee are possible.

3).Of 13 cards, grouping can be done as : 13C5.8C4.4C3.1C1=1287.70.4.1=360360, which is number of ways of grouping 13 cards in a groups of 5-4-3-1.

Also this question can be further extended by saying the number of ways of selecting a hand. That can be done in 52C13 number of ways.

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