The exponent of 7 in `.^(100)C_(50)` is

Options

A. 0
B. 2
C. 4
D. none of these

Answer

A

Explanation

We have, `""^(100)C_(50)=(1000!)/(50!50!)`
Now,
`E_(7)(100!)=[(100)/(7)]+[(100)/(7^(2))]=14+2=16`
and, `E_(7)(50!)=[(50)/(7)]+[(50)/(7^(2))]=7+1=8`
Thus, exponent of 7 in `""^(100)C_(50)=16-2xx8=0`