What is the number of ways of choosing 4 cards from a pack of 52 cards. In how many of these cards are either red or black.
 

Asked by kuriakose7600 | 2nd Jan, 2016, 11:24: PM

Expert Answer:

begin mathsize 14px style N u m b e r space o f space w a y s space o f space c h o o s i n g space 4 space c a r d s space f r o m space a space p a c k space o f space 52 space c a r d s equals C presuperscript 52 subscript 4 equals fraction numerator 52 factorial over denominator 48 factorial 4 factorial end fraction equals fraction numerator 52 cross times 51 cross times 50 cross times 49 over denominator 4 cross times 3 cross times 2 cross times 1 end fraction equals 13 cross times 17 cross times 25 cross times 49 equals 270725  end style
begin mathsize 14px style Number space of space ways space of space choosing space 4 space cards space either space black space or space red equals fraction numerator straight C presuperscript 26 subscript 4 cross times straight C presuperscript 26 subscript 0 plus straight C presuperscript 26 subscript 3 cross times straight C presuperscript 26 subscript 1 plus straight C presuperscript 26 subscript 2 cross times straight C presuperscript 26 subscript 2 plus straight C presuperscript 26 subscript 1 cross times straight C presuperscript 26 subscript 3 plus straight C presuperscript 26 subscript 0 cross times straight C presuperscript 26 subscript 4 over denominator straight C presuperscript 52 subscript 4 end fraction equals fraction numerator 14950 cross times 1 plus 2600 cross times 26 plus 325 cross times 325 plus 26 cross times 2600 plus 1 cross times 14950 over denominator 270725 end fraction equals fraction numerator 14950 plus 67600 plus 105625 plus 67600 plus 14950 over denominator 270725 end fraction equals 270725 over 270725 equals 1 end style

Answered by Rashmi Khot | 4th Jan, 2016, 10:46: AM

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