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Permutation And Combination

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Introduction

☼ Factorials  :   Permutation and Combination is a topic which requires use of  the concept of  factorials. A factorial is the number obtained by multiplying all the positive integers less than or equal to a given positive integer. The factorial of  a given integer n is usually written as n ! or   n   .

 n !   =    n \times (n – 1) \times (n – 2) \times … \times 3 \times 2 \times 1

=    1  \times  2  \times 3  \times . . . \times  (n – 2) \times (n – 1) \times n

A factorial is only defined for positive whole numbers.

0 !  =  1 !  =  1    &     n !  =  n (n – 1) !

 e.g. (i) What is  9 ! ?

  Soln. 9 !  =   9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1  =  362880.

  (ii) What is  \frac{10!}{8!}  ?

  Soln.  \frac{10!}{8!}  =  \left (\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 }{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 } \right ) =  \left (\frac{10 \times 9 \times 8!}{8!} \right )  =  10 \times 9  =  90.

 

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