Question

Simplify the expression. 10C7

A. 1

B. 3,628,800

C. 604,800

D. 120

Answer 1

120

Explanation:

Answer 2

Combination

Explanation:

Here by 10C7 we actually mean,
`C_(7)^(10)`

And the formula for evaluating mCn is

`=(m!)/(n!*(m-n)!)`

Therefore

10C7 =

`=(10!)/(7!*(10-7)!) \\=(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

`=(10*9*8*7*.....3*2*1)/((3*2*1)*(7*6*5....3*2*1))\\=(10*9*8)/(3*2*1) \\=(10*3*4)/(1) \\=120`

Hence the answer is D