Mathematics

Question

Evaluate the expression

14!/12!2!

2 Answer

  • [tex]\frac{14!}{12!2!} \\\\ = \frac{14!}{12!} . \frac{1}{2!} \\\\ = (14 \times 13) . \frac{1}{2} \\\\ = \frac{182}{2} \\\\ = 91[/tex]
  • [tex]\frac{14!}{12!2!}[/tex]

    This is what it basically means:
    [tex]=\frac{14*13*12*11*10*9*8*7*6*5*4*3*2*1}{12*11*10*9*8*7*6*5*4*3*2*1(2*1)} [/tex]

    To simplify that, cross out numerators that are the same as the denominators because anything divided by itself equals 1.
    [tex]=\frac{14(13)}{2*1}[/tex]
    Now because anything multiplied by 1 stays the same, this simplifies to
    [tex]=\frac{14(13)}{2}[/tex]
    [tex]=\frac{182}{2}[/tex]
    [tex]=91[/tex]