Answer:
Combination
Step-by-step explanation:
Here by 10C7 we actually mean, [tex]C_{7}^{10}[/tex]
And the formula for evaluating mCn is
[tex]=\frac{m!}{n!*(m-n)!}[/tex]
Therefore
10C7 =
[tex]=\frac{10!}{7!*(10-7)!} \\=\frac{10!}{7!*3!} \\[/tex]
Where m! is called m factorial and can be evaluated as
m!= m*(m-1)*(m-2)*(m-3)*.......3*2*1
Hence
10!= 10*9*8......*3*2*1
7!= 7*8*6.....3*2*1
3!=3*2*1
With these we can evaluate
10C7
[tex]=\frac{10*9*8*7*.....3*2*1}{(3*2*1)*(7*6*5....3*2*1)}\\=\frac{10*9*8}{3*2*1} \\=\frac{10*3*4}{1} \\=120[/tex]
Hence the answer is D
