Question

Simplify the expression. 10C7 A. 1 B. 3,628,800 C. 604,800 D. 120

Answer 1

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)*.......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

$=\frac{10*9*8*7*.....3*2*1}{(3*2*1)*(7*6*5....3*2*1)}\\=\frac{10*9*8}{3*2*1} \\=\frac{10*3*4}{1} \\=120$

Hence the answer is D