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The exponent of 7 in 100 C 50 is

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Solution:   ^100C_50=frac100!50! imes 50!

               Rightarrow         E_7(100!)  = The exponent of 7 in (100!)

               Rightarrow         E_7(100!)=[frac1007+frac1007^2]=14+2=16.

                           E_7(50!)=[frac507+frac507^2]=7+1=8.

                herefore          E_7(^100C_50) =  The exponent of 7 in (^100C_50)

               Rightarrow                            =16-(8+8)=0.  

Posted by

Deependra Verma

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