fozzzy wrote:

What is the product of all positive odd integers less than 10000?

A) \(\frac{10000!}{{(5000!)^2}}\)

B) \(\frac{10000!}{2^{5000}}\)

C) \(\frac{9999!}{2^{5000}}\)

D) \(\frac{10000!}{2^{5000}. 5000!}\)

E) \(\frac{5000!}{2^{5000}}\)

Product of all odd positive integers less than 10000 is 1*3*5*7.......*9999

which can be written as (1*2*3*4.....10000)/2*4*6*...*10000

where as 2*4*6*...*10000=(2^5000)(1*2*3*....*5000)...since 2 is taken as common from 2,4,6,8,..10000 which has 5000 terms

given equation becomes (1*2*3*4*....*10000)/(2^5000)(1*2*3*....*5000)

=>10000!/(2^5000)(5000!)

Ans D...Hope my logic is right