Question

If "C4 = 210, then the value of'n' is
a) 210
b) 4
c) 6
d) 10​

Answer 1

Answer:

nC3 = 35.

n!/[3!.(n-3)! =35

n.(n-1).(n-2).(n-3)!/3.2.1.(n-3)! =35

n.(n-1).(n-2)=210.

n.(n^2–3n+2)-210=0

n^3–3n^2+2n-210=0.

put n =7 ,R=343–147+14–210=357–357=0.

n-7 is a factor .

n^3 -3n^2 +2n-210=0

or n^2(n-7)+4n(n-7)+30(n-7) =0.

or (n-7) (n^2+4n+30)=0.

Either n-7 =0 => n= 7 . Answer.

Or n^2+4n+30 =0.

D = (4)^2–4.1.30= -104 = ( negative ).

roots are imaginary.

n = 7 . Answer.

Answer 2

1. The value of n is 10 because C4÷n
2. 210÷10=21.