Question

find the exponent of 7 in 100C50

Answer 1

100c50 = 100!/50!*50!
here is a trick to check exponents of any number in factorial
let say if we want to check exponents of 5 in 100!
just simply divide 100/5 = 20
then
20 /5 = 4
4/5 = no divide
so exponents of 5 in 100! = 20+4 = 24
now same as to check the exponents of 7 in 100!
100/7 = 14.28
14/7 = 2
thus 14 +2 = 16
there will be 16 exponents of 7 in 100!
now , to check exponents of 7 in 50!
50/7 = 7.14
7/7 = 1
7+1 = 8
thus 8 exponents in one 50!
in two 50! exponents of 7 will be 2*8 = 16
in numerator there is 16 exponents of 7
and in denominator too
thus exponents of 7 in 100c50 will be 0