Permutations And Combinations

Question
CBSEENMA11014103

How many 3-digit numbers can be formed by using digits 1 to 9 if no digit is repeated?  

Solution

Number of digits available = 9
(1, 2, 3, 4, 5, 6, 7, 8, 9)
Number of digits to be used = 3
(No digit is to repeat)
                      
rightwards double arrow                      n = 9,  r = 3
Number of permutations = space space space straight P presuperscript 9 subscript 3 space equals space fraction numerator 9 factorial over denominator 6 factorial end fraction space equals space fraction numerator 9 cross times 8 cross times 7 cross times 6 factorial over denominator 6 factorial end fraction equals 504
Hence, the number of 3-digit numbers formed = 504.

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