Answer:
Combination
Step-by-step explanation:
Here by 10C7 we actually mean, \(C_{7}^{10}\)
And the formula for evaluating mCn is
\(=\frac{m!}{n!*(m-n)!}\)
Therefore
10C7 =
\(=\frac{10!}{7!*(10-7)!} \\=\frac{10!}{7!*3!} \\\)
Where m! is called m factorial and can be evaluated as
m!= m(m-1)(m-2)(m-3).......321
Hence
10!= 1098......321
7!= 786.....321
3!=32*1
With these we can evaluate
10C7
\(=\frac{10*9*8*7*.....3*2*1}{(3*2*1)*(7*6*5....3*2*1)}\\=\frac{10*9*8}{3*2*1} \\=\frac{10*3*4}{1} \\=120\)
Hence the answer is D
