Cancel from numerator and denominator
(12*11*10*9*8)/(5*4*3*2*1)
so 5*2 is 10 - that cancels
and 4*3 is 12 - that cancels ..u r left with 3 integers in the numerator. Hence III. 12!/(7!)(5!) is also an integer
Factorial Question
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ronniecoleman
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12! / 5! 7!
Have a rule if a!/b!d! if a = b+ d
then a!/b!d! is a integer !
otherwise...we need to check it out
Have a rule if a!/b!d! if a = b+ d
then a!/b!d! is a integer !
otherwise...we need to check it out
Admission champion, Hauz khaz
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011-27565856
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parallel_chase
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Here is another rule
Product of n consecutive integers will always be divisible by n!
12! /5! 7!
we know that 7! cancels out, whats left is
(8*9*10*11*12)/5!
if we follow the above rule, we have product of 5 consecutive integers, therefore the result will be an integer.
Hope this helps.
Product of n consecutive integers will always be divisible by n!
12! /5! 7!
we know that 7! cancels out, whats left is
(8*9*10*11*12)/5!
if we follow the above rule, we have product of 5 consecutive integers, therefore the result will be an integer.
Hope this helps.
No rest for the Wicked....
The value of option III is nothing but the value of 12C7 which always comes as integer or you can see that after canceling 7! we are left with 5! in denominator which is equal to 120 and in numerator it comes from product of 12 and 10 so it comes as integer . Hence all the values are integersawilhelm wrote:Which of the following is an integer?
I. 12!/6!
II. 12!/8!
III. 12!/(7!)(5!)
Is there a quick way to calculate whether III is an integer? After canceling out 7-1 I'm left with
(12*11*10*9*8)/(5*4*3*2*1)
Thank you!
P. V. Singh
+ve Approach, +ve Attitude will give +ve result.
+ve Approach, +ve Attitude will give +ve result.
