Answer: A. 210
Step-by-step explanation:
We know that the number of combinations of n things taking r at time is given by expression :-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex] (1)
The given expression : [tex]^{10}C_{6}[/tex] which basically gives the number of combinations of 10 things taking 6 at a time.
Using (1) , we have
[tex]^{10}C_{6}=\dfrac{10!}{6!(10-6)!}\\\\=\dfrac{10\times9\times8\times7\times6!}{6!4!}\\\\=\dfrac{10\times9\times8\times7}{4!}\ \ [\text{Cancel }6!\text{ from numerator and denominator}]\\\\=\dfrac{10\times9\times8\times7}{4\times3\times2\times1}\\\\=210[/tex]
Hence, the correct answer is A. 210 .
