Question

23. If n is a positive integer, the notation n! (read "n factorial”) is used to represent the
product of the integers from 1 to n inclusive. For example, 5! = 1x2x3x4x5 = 120.
Which of the following is equal to a perfect square?
(A) (20)!(19)!/1
(B) (20)!(19)! /2 (20)!(19)!/3 (D) (20)!(19)!/4 (E) (20)!(19)!/5​

Answer 1

Answer:

we know that

n!=(n) (n-1)!

so

in the question,

20! can be written as 20×19!

since in all the options there is

20! and 19!

therefore writhing 20! as 20×19!

would cancel out both the 19!.

So it depends on 20 and the second number.

in first option

we get

20/1=20 which is not perfect square.

in second option,

20/2=10 not perfect square.

third option,

20/4=5 not perfect square

fourth option

20/5=4 WHICH IS PERFECT SQUARE.

Therefore option D is correct.

Please mark it as brainliest.