N=(1!)(2!)(3!)(4!)(5!)(6!)(7!)(8!)(9!)

1!=1

2!=1*2

3!=1*2*3

4!=1*2*3*4

5!=1*2*3*4*5

6!=1*2*3*4*5*6

7!=1*2*3*4*5*6*7

8!=1*2*3*4*5*6*7*8

9!=1*2*3*4*5*6*7*8*9

N=(2^8)(3^7)(4^6)(5^5)(6^4)(7^3)(8^2)(9^1)

=(2^30)(3^13)(5^5)(7^3)

To find the number of perfect squares each exponent in the prime factorization must be even .

Comparing to the form (2^p)(3^q)(5^r)(7^s).

In this case,

p can take values from 0 to 30

q can take values from 0 to 13

r can take values from 0 to 5

s can take values from 0 to 3

Number of even exponents

p=16

q=7

r=3

s=2

Number of perfect squares= 16*7*3*2 = 672

Answer B

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