Question

What is the value of the expression 10 C 6? A.210 B.720 C.5040 D.151,200

Answer 1

are you asking 10 x C(5040) x 6?? 

Answer 2

Answer: A. 210

Explanation:

We know that the number of combinations of n things taking r at time is given by expression :-

`^nC_r=(n!)/(r!(n-r)!)` (1)

The given expression :
`^(10)C_(6)` which basically gives the number of combinations of 10 things taking 6 at a time.

Using (1) , we have

`^(10)C_(6)=(10!)/(6!(10-6)!)\\\\=(10*9*8*7*6!)/(6!4!)\\\\=(10*9*8*7)/(4!)\ \ [\text{Cancel }6!\text{ from numerator and denominator}]\\\\=(10*9*8*7)/(4*3*2*1)\\\\=210`

Hence, the correct answer is A. 210 .