What is the mnimum number of ways of choosing 4 cards from a pack of 52 playing cards? in how many of these:
1) are 4 card of the same suit?
2)do 4 cards belong to 4 different suits?
[I found the answer to 1) as 13C4+13C4+ 13C4+ 13C4. but when I don't understand how to solve question number 2. According to solutions it is given as 13C1 x 13C1 x 13C1 x 13C1= 13^4.
I understand how we got 13C1 but I don't understand why multiplication was used and not division]
Asked by Deebu
31st January 2015,
6:55 PM
Answered by Expert
Answer:
There are 13 cards in a suit.
And there are 4 suits.
We need to select 4 cards belong to 4 different suits.
Selection of one card from one suit can be done in 13C1 = 13 ways.
Selection of second card from another suit can be done in 13C1 = 13 ways.
Selection of thrid card from another suit can be done in 13C1 = 13 ways.
Selection of fourth card from another suit can be done in 13C1 = 13 ways.
We know that if there are two jobs such that one of them can be completed in m ways and when it has been completed in any one of
these m ways, second job can be completed in n ways, then the tow jobs in succession can be completed in m x n ways.-Fundamental Principle of multiplication
Thus, selection of 4 cards from 4 different suits can be done in 13C1 x 13C1 x 13C1 x 13C1 = 134 ways.
Answered by Expert
1st February 2015,
7:16 AM
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