If 100C2 has a value of 4,950, what is the value of 100C98?

Question

A. 4,950
B. 9,900
C. 49,5000
D. 99,000

Answer 1

A is the correct answer.
Out of 100 you can chose 2, the same number of ways as you can leave out 2. Therefore 100C2 can not be different from 100C98.

Answer 2

The answer is C, I am thinking

There is a pattern here:
Answer = 100C2 * (2 + 98) = (100C2)*100 = 4950 * 100 = 495000

Therfore you always add 2 to the new number
If you were looking for 100C92 as an example:
100C92 = 100C2* (2+92) = 4950 * 94 = 465300

Answer 3

It is also 4,950.

If I were going to pick 2 marbles out of 100, that's the same as putting 98 marbles aside and seeing what 2 are left.

So 100C2 = 100C98.

In general nCk = nC(n-k)

The expanded form of nCk is:
n! / k! (n-k)!

So 100! / 2! 98! is the same as 100! / 98! 2!

The answer is:
A. 4,950

Answer 4

100C2 = (100!)/(2!(100 - 2)!)
100C2 = (100!)/(2! * 98!)
100C2 = 4950

100C98 = (100!)/(98!(100 - 98)!)
100C98 = (100!)/(98! * 2!)
100C98 = 4950

Ans : A. 4,950

Answer 5

If your question is written to mean:

100 x C x 2 = 4950

then C = 24.75

And,

100 x C x 98 = 242,550

zahbudar

Answer 6

Normal has the correct answer, but you could also calculate 100!/(98!*(2!)) (or look at it and realize that multiplication is cummutative so 98!*2! is the same as 2!*98!)

Best figure it out out before exams ☺


Doug

Answer 7

nCr = nC(n-r)

so, 100C2 = 100C98

Answer 8

this question does not mean anything to me

100C2?

clearly it is not 100*c*2 where "c" is an algebraic variable, so

what does it represent?